2019
14
1
0
210
1

Certain Inequalities for a General Class of Analytic and Biunivalent Functions
https://scma.maragheh.ac.ir/article_34894.html
10.22130/scma.2018.70945.277
1
In this work, the subclass of the function class S of analytic and biunivalent functions is defined and studied in the open unit disc. Estimates for initial coefficients of Taylor Maclaurin series of biunivalent functions belonging these class are obtained. By choosing the special values for parameters and functions it is shown that the class reduces to several earlier known classes of analytic and biunivalent functions studied in the literature. Coclusions are given for all special parameters and the functions. And finally, some relevant classes which are well known before are recognized and connections to previus results are made.
0

1
13


Arzu
Akgul
Department of Mathematics, Faculty of Arts and Science, Kocaeli University, Kocaeli, Turkey.
Iran
akgulcagla@hotmail.com
Analytic functions
Biunivalent functions
Coefficient bounds and coefficient estimates
TaylorMaclaurin coefficients
[[1] A. Akgul, and S. Altinkaya, Coefficient estimates associated with a new subclass of biunivalent functions, Acta Univ. Apulensis Math. Inform, 52 (2017), pp. 121128.##[2] A. Akgul, Finding initial coefficients for a class of biunivalent functions given by qderivative, AIP Conference Proceedings, Vol. 1926. No. 1. AIP Publishing, 2018.##[3] A. Akgul, New subclasses of analytic and biunivalent functions involving a new integral operator defined by polylogarithm function, Theory Appl. Math. Comput. Sci., 7 (2017), pp. 3140.##[4] A. Akgul, Coefficient estimates for certain subclass of biunivalent functions obtained with polylogarithms, Mathematical Sciences And Applications ENotes, 6 (2018), pp. 7076.##[5] S. Altinkaya, S. Yalcin, Coefficient bounds for a general subclass of biunivalent functions, Le Matematiche, LXXI, Fasc., I (2016), pp. 8997##[6] D.A. Brannan, T.S. Taha, On some classes of biunivalent functions, in: S.M. Mazhar, A. Hamoui, N.S. Faour (Eds.), Math. Anal. and Appl., Kuwait; February 1821, 1985, in: KFAS Proceedings Series, vol.3, Pergamon Press, Elsevier Science Limited, Oxford, 1988, pp. 5360. see also Studia Univ. BabesBolyai Math., 31 (1986), pp. 7077.##[7] D. A. Brannan and J. G. Clunie, Aspects of comtemporary complex analysis, (Proceedings of the NATO Advanced Study Instute Held at University of Durham:July 120, 1979). New York: Academic Press, (1980).##[8] S. Bulut, Faber polynomial coefficient estimates for a subclass of analytic biunivalent functions, Filomat, 30 (2016), pp. 15671575.##[9] M. Caglar, Halit Orhan, Nihat Yagmur, Coefficient bounds for new subclasses of biunivalent functions, Filomat, 27 (2013), pp. 11651171.##[10] E. Deniz, M. and H. Orhan, The FeketeSzego problem for a class of analytic functions defined by DziokSrivastava operator, Kodai Math. J., 35 (2012), pp. 439462.##[11] B. A. Frasin and M. K. Aouf, New subclasses of biunivalent functions, Appl. Math. Lett., 24 (2011), pp. 15691573.##[12] M. Lewin, On a coefficient problem for biunivalent functions, Proceeding of the American Mathematical Society, 18 (1967), pp. 6368.##[13] E. Netanyahu, The minimal distance of the image boundary from the orijin and the second coefficient of a univalent function in z<1, Arch. Ration. Mech. Anal., 32 (1969), pp. 100112.##[14] Ch. Pommerenke, Univalent functions, Vandenhoeck and Rupercht, Gottingen, 1975.##[15] H. M. Srivastava, A. K. Mishra, and P. Gochhayat, Certain subclasses of analytic and biunivalent functions, Applied Mathematics Letters, 23 (2010), pp. 11881192.##[16] H. M. Srivastava, S. Sumer Eker and R. M. Ali, Coefficient bounds for a certain class of analytic and biunivalent functions, Filomat, 29 (2015), pp. 18391845.##[17] Q.H. Xu, Y.C. Gui and H. M. Srivastava, Coefficient estimates for a certain subclass of analytic and biunivalent functions, Appl. Math. Lett., 25 (2012), pp. 990994.##[18] Q.H. Xu, H.G. Xiao and H. Srivastava, A certain general subclass of analytic and biunivalent functions and associated coefficient estimate problems, Appl. Math. Comput., 218 (2012), pp. 461 465.##]
1

Common Fixed Point in Cone Metric Space for $mathbf{s}mathbf{varphi}$contractive
https://scma.maragheh.ac.ir/article_34861.html
10.22130/scma.2018.65773.251
1
Huang and Zhang cite{Huang} have introduced the concept of cone metric space where the set of real numbers is replaced by an ordered Banach space. Shojaei cite{shojaei} has obtained points of coincidence and common fixed points for sContraction mappings which satisfy generalized contractive type conditions in a complete cone metric space.In this paper, the notion of complete cone metric space has been introduced. We have defined $sphi$contractive and obtained common fixed point theorem for a mapping $f,s$ which satisfies $sphi$contractive.
0

15
26


Hamid
Shojaei
Department of Mathematics, Afzale Kermani, Institute of Higher Education,, Kerman, Iran.
Iran
hshojaei2000@yahoo.com


Neda
Shojaei
Department of Mathematics, Afzale Kermani, Institute of Higher Education, Kerman, Iran.
Iran
n.shojaee64@yahoo.com


Razieh
Mortazaei
Department of Mathematics, Afzale Kermani Institute of Higher Education, Kerman, Iran.
Iran
hshojaei2000@gmai.com
Complete cone metric spaces
Coincidence points
$phi$contraction
$s$contraction mappings
[[1] M. Abbas and G. Jungck, Common fixed point results for noncommuting mappings without continuity in cone metric spaces, J. Math. Anal. Appl., 341 (2008), pp. 416420.##[2] D.W. Boyd and J.S.W. Wong, On nonlinear contractions, Proc. Amer. Math. Soc. 20 (1969), pp. 458464.##[3] C. Di Bari and P. Vetro, $phi$pairs and common fixed points in cone metric spaces, Rend. Circ. Mat. Palermo, 57 (2008), pp. 279285.##[4] L. G. Huang and X. Zhang, Cone metric spaces and fixed point theorems of contractive mappings, J. Math. Anal. Appl., 332 (2007), pp. 14681476.##[5] D. Ilic and C.V. Rakocevi, Common fixed points for maps on cone metric space, J. Math. Anal. Appl., 341 (2008), pp. 876882.##[6] E. Karapinar, Fixed point theory for cyclic $phi$contractions, Appl. Math. Lett, 24 (2011), pp. 822825.##[7] W.A. Kirk, P.S. Srinivasan, and P. veeramany, Fixed point theorem for mapping satisfying cycle contractive condition, Fixed point theory, 4 (2003), pp. 7989.##[8] R.P. Pant, Common fixed points for contractive maps, J. Math. Anal. Appl. 226 (1998), pp. 251251.##[9] H. Shojaei, Some Theorem for Common Fixed Point for SContraction Mappings in Complete Cone Metric Spaces, International Journal on Recent and Innovation Trends in Computing and Communication (IJRITCC), 5 (2017), pp. 241251.##[10] H. Shojaei and R. Mortezaei, Common Fixed Point for Affine Self Maps Invariant Approximation in pnormed Spaces, J. Math. Computer Sci., 6 (2013), pp. 201209.##[11] D. Turkoglu, Cone metric spaces and fixed diametrically contractive mapping, Acta Math. Sin. (Engl. Ser.), 26 (2010), pp. 489496.##[12] P. Vetro, Common fixed points in cone metric spaces, Rend. Circ. Mat. Palermo (2), 56 (2007), pp. 464468.##]
1

Functors Induced by Cauchy Extension of C$^ast$algebras
https://scma.maragheh.ac.ir/article_34860.html
10.22130/scma.2018.73698.306
1
In this paper, we give three functors $mathfrak{P}$, $[cdot]_K$ and $mathfrak{F}$ on the category of C$^ast$algebras. The functor $mathfrak{P}$ assigns to each C$^ast$algebra $mathcal{A}$ a preC$^ast$algebra $mathfrak{P}(mathcal{A})$ with completion $[mathcal{A}]_K$. The functor $[cdot]_K$ assigns to each C$^ast$algebra $mathcal{A}$ the Cauchy extension $[mathcal{A}]_K$ of $mathcal{A}$ by a nonunital C$^ast$algebra $mathfrak{F}(mathcal{A})$. Some properties of these functors are also given. In particular, we show that the functors $[cdot]_K$ and $mathfrak{F}$ are exact and the functor $mathfrak{P}$ is normal exact.
0

27
53


Kourosh
Nourouzi
Faculty of Mathematics, K. N. Toosi University of Technology, Tehran, Iran.
Iran
nourouzi@kntu.ac.ir


Ali
Reza
Faculty of Mathematics, K. N. Toosi University of Technology, Tehran, Iran.
Iran
alireza.lida@yahoo.com
PreC$^ast$ algebras
Extensions of C$^ast$ algebras
Exact functors
Cauchy extension
[[1] W. Arveson, Notes on extensions of $C$*algebras, Duke Math. J., 44 (1977), pp. 329355.##[2] R.G. Bartle, The elements of real analysis. Second edition, John Wiley & Sons, New YorkLondonSydney, 1976.##[3] B. Blackadar, Operator algebras. Theory of $C$*algebras and Von Neumann algebras, Encyclopaedia of Mathematical Sciences, 122. Operator Algebras and Noncommutative Geometry, III. SpringerVerlag, Berlin, 2006.##[4] D.P. Blecher and C. Le Merdy, Operator algebras and their modules an operator space approach, London Mathematical Society Monographs. New Series, 30. Oxford Science Publications. The Clarendon Press, Oxford University Press, Oxford, 2004.##[5] L.G. Brown, R.G. Douglas and P.A. Fillmore, Extensions of $C$*algebras and $K$homology, Ann. of Math., 105 (1977), pp. 265324.##[6] R.C. Busby, Double centralizers and extensions of $C$*algebras, Trans. Amer. Math. Soc., 132 (1968), pp. 7999.##[7] J.B. Conway, A course in functional analysis, Graduate Texts in Mathematics, 96. SpringerVerlag, New York, 1985.##[8] J. Dieudonne, Foundations of modern analysis. Enlarged and corrected printing, Pure Appl. Math., Vol. 10I. Academic Press, New YorkLondon, 1969.##[9] J. Dugundji, An extension of Tietze's theorem, Pacific J. Math., 1 (1951), pp. 353367.##[10] G.G. Kasparov, The operator $K$functor and extensions of $C$*algebras, (Russian) Izv. Akad. Nauk SSSR Ser. Mat., 44 (1980), pp. 571636.##[11] S. MacLane, Categories for the working mathematician, Graduate Texts in Mathematics, Vol. 5. SpringerVerlag, New YorkBerlin, 1971.##[12] G.J. Murphy, $C$*algebras and operator theory, Academic Press, Inc., Boston, MA, 1990.##[13] G.A. Reid, Epimorphisms and surjectivity, Invent. Math., 9 (1969/1970), pp. 295307.##[14] J.J. Rotman, An introduction to homological algebra, Second edition. Universitext. Springer, New York, 2009.##[15] W. Rudin, Principles of mathematical analysis, Third edition. International Series in Pure and Applied Mathematics, McGrawHill Book Co., New YorkAucklandDCsseldorf, 1976.##[16] K.W. Yang, Completion of normed linear spaces, Proc. Amer. Math. Soc., 19 (1968), pp. 801806.##]
1

Admissible Vectors of a Covariant Representation of a Dynamical System
https://scma.maragheh.ac.ir/article_34859.html
10.22130/scma.2018.72232.291
1
In this paper, we introduce admissible vectors of covariant representations of a dynamical system which are extensions of the usual ones, and compare them with each other. Also, we give some sufficient conditions for a vector to be admissible vector of a covariant pair of a dynamical system. In addition, we show the existence of Parseval frames for some special subspaces of $L^2(G)$ related to a uniform lattice of $G$.
0

55
61


Alireza
Bagheri Salec
Department of Mathematics, Faculty of Science, University of Qom, Qom, Iran.
Iran
alireza_bagheri_salec@yahoo.com


Seyyed Mohammad
Tabatabaie
Department of Mathematics, Faculty of Science, University of Qom, Qom, Iran.
Iran
smtabatabaei@qom.ac.ir


Javad
Saadatmandan
Department of Mathematics, Faculty of Science, University of Qom, Qom, Iran.
Iran
jsaadatmandan@yahoo.com
Admissible vector
Covariant representation
Dynamical system
[[1] G.B. Folland, A Course in Abstract Harmonic Analysis, CRC Press., London, 1995.##[2] H. Fuhr, Abstract Harmonic Analysis of Continuous Wavelet Transforms, SpringerVerlag, Berlin, 2005.##[3] A. Grossmann, J. Morlet, and T. Paul, Transforms associated to square integrable group representations I, J. Math. Phys., 26 (1985), pp. 24732479.##[4] P.E.T. Jorgensen, K.D. Merrill and J.A. Packer, Representations, Wavelets and Frames, Applied and Numerical Harmonic Analysis, Birkhäuser, 2008.##[5] A. Khosravi and B. Khosravi, Frames and bases in tensor products of Hilbert spaces and Hilbert $C^*$modules, Proc. Indian Acad. Sci., 117 (2003), pp. 112.##[6] B.H. Sadathoseyni and S.M. Tabatabaie, Coorbit spaces related to locally compact hypergroups, Acta Math. Hungar., 153 (2017), pp. 177196.##[7] S.M. Tabatabaie and S. Jokar, A characterization of admissible vectors related to representations on hypergroups, Tbil. Math. J., 10 (2017), pp. 143151.##[8] D.P. Williams, Crossed Products of $C^*$Algebras, Mathematical surveys and monographs, 2007.##]
1

On Periodic Shadowing Property
https://scma.maragheh.ac.ir/article_34858.html
10.22130/scma.2018.69088.270
1
In this paper, some properties of the periodic shadowing are presented. It is shown that a homeomorphism has the periodic shadowing property if and only if so does every lift of it to the universal covering space. Also, it is proved that continuous mappings on a compact metric space with the periodic shadowing and the average shadowing property also have the shadowing property and then are chaotic in the sense of LiYorke. Moreover, any distal homeomorphisms on a compact metric space with the periodic shadowing property do not have the asymptotic average shadowing property.
0

63
72


Ali
Darabi
Department of Mathematics, Faculty of Mathematical and Computer Sciences, Shahid Chamran University of Ahvaz, P.O. Box 6135743135, Ahvaz, Iran.
Iran
darabi233@yahoo.com
Periodic shadowing
Shadowing
Chain transitive
Distal
[[1] J. Blanks, J. Brooks, G. Cairns, G. Davis, and P. Stacey, On Devaney's definition of chaos, Amer. Math. Monthly, 99 (1992), pp. 332334.##[2] M.L. Blank, Small perturbations of chaotic dynamical systems, Russian Math. Surveys, 44 (1989), pp. 133.##[3] B. Carvalho, Twosided limit shadowing Property, Ph.D. Thesis, Universidade Federal do Rio de Janeiro, 2015.##[4] A. Darabi and F. Forouzanfar, Periodic Shadowing and standard shadowing property, AsianEuropean J. Math., 10 (2017).##[5] R. Gu, The asymptotic average shadowing property and transitivity, J. Nonlinear Analysis., 67 (2007), pp. 16801689.##[6] K. Hiraide, Expansive homeomorphisms with the pseudoorbit tracing property of ntori, J. Math. Soc. Japan., 41 (1989), pp. 357389.##[7] W. Huang and X. Ye, Devaney's chaos or 2scattering implies LiYork's chaos, Topology Appl., 117 (2002), pp. 259272.##[8] A. Iwanik, Independent sets of transitive points, in Dynamical Systems and Ergodic Theory, Vol. 23 (Banach Center Publications, Warsaw, 1989), pp. 277282.##[9] A. Koropecki and E. Pujals, Some consequences of the shadowing property in low dimensions, Ergodic Theory and Dynamical Systems., 195 (2013), pp. 137.##[10] P. Koscielniak, On genericity of shadowing and periodic shadowing property, J. Math. Anal. Appl., 310 (2005), pp. 188196.##[11] M. Kulczycki, D. Kwietniak, and P. Oprocha, On almost specification and average shadowing properties, Fund. Math., 224 (2014), pp. 241278.##[12] A.V. Osipov, S.Yu. Pilyuginm, and S.B. Tikhomirov, Periodic shadowing and $Omega$stability, Regular and Chaotic Dynamics, 15 (2010), pp. 404417.##[13] K. Palmer, Shadowing in Dynamical Systems., Theory and Applications, Kluwer, Dordrecht, 2000.##[14] S.Yu. Pilyugin, Shadowing in Dynamical Systems, Lect. Notes in Math., SpringerVerlag, Berlin, 1999.##[15] O.B. Plamenevskaya, Weak shadowing for twodimensional diffeomorphisms, Mat. Zametki., 65 (2013), pp. 477480.##]
1

FeketeSzegö Problem of Functions Associated with Hyperbolic Domains
https://scma.maragheh.ac.ir/article_34490.html
10.22130/scma.2018.75275.329
1
In the field of Geometric Function Theory, one can not deny the importance of analytic and univalent functions. The characteristics of these functions including their taylor series expansion, their coefficients in these representations as well as their associated functional inequalities have always attracted the researchers. In particular, FeketeSzegö inequality is one of such vastly studied and investigated functional inequality. Our main focus in this article is to investigate the FeketeSzegö functional for the class of analytic functions associated with hyperbolic regions. Tofurther enhance the worth of our work, we include similar problems for the inverse functions of these discussed analytic functions.
0

73
88


Sarfraz Nawaz
Malik
COMSATS University Islamabad, Wah Campus, Pakistan.
Iran
snmalik110@yahoo.com


Sidra
Riaz
COMSATS University Islamabad, Wah Campus, Pakistan.
Iran
iman.iman1993@yahoo.com


Mohsan
Raza
Government College University, Faisalabad, Pakistan.
Iran
mohsan976@yahoo.com


Saira
Zainab
University of Wah, Wah Cantt, Pakistan.
Iran
sairazainab07@yahoo.com
Analytic functions
Starlike functions
Convex functions
FeketeSzegö problem
[[1] O.P. Ahuja and M. Jahangiri, FeketeSzegö problem for a unified class of analytic functions, Panamer. Math. J., 7 (1997), pp. 6778.##[2] M. Fekete and G. Szegö, Eine bemerkung uber ungerade schlichte funktionen, J. London Math. Soc., 8 (1933), pp. 8589.##[3] A.W. Goodman, On uniformly convex functions, Ann. Polon. Math., 56 (1991), pp. 8792.##[4] A.W. Goodman, Univalent Functions, vol. III, Mariner Publishing Company, Tempa, Florida, USA, 1983.##[5] W. Haq, S. Mehmood, and M. Arif, On analytic functions with generalized bounded Mocanu variation in conic domain, Mathematica Slovaca, 67 (2017), pp. 401410.##[6] S. Hussain, M. Arif, and S.N. Malik, Higher order closetoconvex functions associated with AttiyaSriwastawa operator, Bull. Iranian Math. Soc., 40 (2014), pp. 911920.##[7] S. Kanas, An unified approach to the FeketeSzegö problem, Appl. Math, Comput., 218 (2012), pp. 84538461.##[8] S. Kanas, Coefficient estimates in subclasses of the Caratheodory class related to conical domains, Acta Math. Univ. Comenian., 74 (2005), pp. 149161.##[9] S. Kanas and A. Wisniowska, Conic domains and starlike functions, Rev. Roumaine Math. Pures Appl., 45 (2000), pp. 647657.##[10] S. Kanas and A. Wisniowska, Conic regions and kuniform convexity, J. Comput. Appl. Math., 105 (1999), pp. 327336.##[11] F.R. Keogh and E.P. Merkes, A coefficient inequality for certain classes of analytic functions, Proc. Amer. Math. Soc., 20 (1969), pp. 812.##[12] W. Koepf, On the FeketeSzegö problem for close to convex functions I, Proc. Amer. Math. Soc., 101 (1987), pp. 8995.##[13] W. Ma and D. Minda, A unified treatment of some special classes of univalent functions, in: Proc. conference on complex analysis, Tianjin, (1992), pp. 157169.##[14] W. Ma and D. Minda, Uniformly convex functions II, Ann. Polon. Math., 8 (1993), pp. 275285.##[15] S. Mahmood, M. Arif, and S.N. Malik, Janowski type closetoconvex functions associated with conic regions, J. Inequal. Appl., 259 (2017), pp. 114.##[16] S. Mahmood, S.N. Malik, S. Farman, S.M.J. Riaz, and S. Farwa, Uniformly AlphaQuasiConvex Functions Defined by Janowski Functions, J. Function Spaces, 2018 (2018), pp. 17.##[17] S. Mahmood, S.N. Malik, S. Mustafa, and S.M.J. Riaz, A new Subclass of kJanowski Type Functions Associated with Ruscheweyh Derivative, J. Function Spaces, 2017 (2017), pp. 17.##[18] S.N. Malik, M. Raza, M. Arif, and S. Hussain, Coefficient estimates of some subclasses of analytic functions related with conic domains, Anal. Stiinti. ale Univer. Ovidius Const., Seria Mate., 21 (2013), pp. 181188.##[19] A.K. Mishra and P. Gochhayat, The FeketeSzegö problem for kuniformly convex functions and for a class defined by the OwaSrivastava operator, J. Math. Anal. Applications, 347 (2008), pp. 563572.##[20] K. I. Noor and S. N. Malik, On coefficient inequalities of functions associated with conic domains, Comput. Math. Appl., 62 (2011), pp. 22092217.##[21] K.I. Noor and S.N. Malik, On generalized bounded Mocanu variation associated with conic domain, Math. Comput. Modell., 55 (2012), pp. 844852.##[22] M. Raza and S.N. Malik, Upper bound of the third Hankel determinant for a class of analytic functions related with lemniscate of Bernoulli, J. Inequal. Appl., 2013 (2013), Article 412.##[23] F. Ronning, On starlike functions associated with parabolic regions, Ann. Univ. Mariae CurieSklodowska, Sect A, 45 (1991), pp. 117122.##[24] F. Ronning, Uniformly convex functions and a corresponding class of starlike functions, Proc. Amer. Math. Soc., 118 (1993), pp. 189196.##[25] J. Sokol and H.E. Darwish, FeketeSzegö problem for starlike and convex functions of complex order, Appl. Math. Letters, 23 (2010), pp. 777782.##]
1

On the Linear Combinations of Slanted HalfPlane Harmonic Mappings
https://scma.maragheh.ac.ir/article_34489.html
10.22130/scma.2018.72574.293
1
In this paper, the sufficient conditions for the linear combinations of slanted halfplane harmonic mappings to be univalent and convex in the direction of $(gamma) $ are studied. Our result improves some recent works. Furthermore, a illustrative example and imagine domains of the linear combinations satisfying the desired conditions are enumerated.
0

89
96


Ahmad
Zireh
Department of Mathematics, Shahrood University of Technology, P.O.Box 31636155, Shahrood, Iran.
Iran
azireh@gmail.com


Mohammad Mehdi
Shabani
Department of Mathematics, Shahrood University of Technology, Shahrood, Iran.
Iran
mohammadmehdishabani@yahoo.com
Harmonic univalent mappings
Linear combination
Slanted halfplane mappings
[[1] D.M. Campbell, A survey of properties of the convex combination of univalent functions, Rocky Mountain J. Math., 5 (1975), pp. 475492.##[2] J. Clunie and T. SheilSmall, Harmonic univalent functions, Ann. Acad. Sci. Fenn. Ser. A I Math., 9 (1984), pp. 325.##[3] M. Dorff, M. Nowak, and M. Wooszkiewicz, Convolutions of harmonic convex mappings, Complex Var. Elliptic Equ., 57 (2012), pp. 489503.##[4] T.H. MacGregor, The univalence of a linear combination of convex mappings, J. London Math. Soc., 44 (1969), pp. 210212.##[5] C. Pommerenke, On starlike and closetoconvex functions, Proc. Lond. Math. Soc., 13 (1963), pp. 290304.##[6] S.Y. Trimble, The convex sum of convex functions, Math. Z., 109 (1969), pp. 112114.##[7] Z.G. Wang, Z.H. Liu, and Y.C. Li, On the linear combinations of harmonic univalent mappings, J. Math. Anal. Appl., 400 (2013), pp. 452459.##]
1

Fuzzy Best Simultaneous Approximation of a Finite Numbers of Functions
https://scma.maragheh.ac.ir/article_34488.html
10.22130/scma.2018.65402.258
1
Fuzzy best simultaneous approximation of a finite number of functions is considered. For this purpose, a fuzzy norm on $Cleft (X, Y right )$ and its fuzzy dual space and also the set of subgradients of a fuzzy norm are introduced. Necessary case of a proved theorem about characterization of simultaneous approximation will be extended to the fuzzy case.
0

97
106


Hossain
Alizadeh Nazarkandi
Department of Mathematics,Marand Branch, Islamic azad university, Marand, Iran.
Iran
halizadeh@marandiau.ac.ir
Fuzzy best Simultaneous approximation
Fuzzy subgradient
Fuzzy dual space
Dual seminorm
[[1] C. Alegre and S. Romaguera, The HahnBanach Extension Theorem for Fuzzy Normed Spaces Revisited, Abstr. Appl. Anal., (2014), article ID 151472.##[2] T. Bag and S.K. Samanta, Finite dimensional fuzzy normed linear spaces, Journal of Fuzzy Mathematics, 11 (2003), pp. 687705.##[3] S.C. Cheng and J.N. Mordeson, Fuzzy linear operators and fuzzy normed linear spaces, Bull. Calcutta Math. Soc., 86 (1994), pp. 429436, .##[4] M. Goudarzi and V.M. Vaezpour, Best Simultaneous approximation in fuzzy normed spaces, Iranian J. of Fuzzy Syst., 7 (2010), pp. 8796.##[5] I. Kramosil and J. Michalek, Fuzzy metrics and statistical metric spaces, Kybernetika, 11 (1975), pp. 336344.##[6] R.T. Rockafellar, Convex Analysis, Princeton Univ. Press, Princeton, NJ, (1970).##[7] B. Schweizer and A. Sklar, Statistical metric spaces, Pac. J. Math., 10 (1960), pp. 313334.##[8] V.M. Vaezpour and F. Karimi, tbest approximation in fuzzy normed spaces, Iranian J. of Fuzzy Syst., 5 (2008), pp. 9399.##[9] G.A. Watson, A Characterization of Best Simultaneous Approximations, J. of Approximation Theory, 75 (1993), pp. 175182 .##[10] G.A. Watson, Characterization of subdifferential of some matrix norm, Linear Algebra Appl., 170 (1992), pp. 3345.##]
1

A Class of Hereditarily $ell_p(c_0)$ Banach spaces
https://scma.maragheh.ac.ir/article_34486.html
10.22130/scma.2018.63393.239
1
We extend the class of Banach sequence spaces constructed by Ledari, as presented in ''A class of hereditarily $ell_1$ Banach spaces without Schur property'' and obtain a new class of hereditarily $ell_p(c_0)$ Banach spaces for $1leq p<infty$. Some other properties of this spaces are studied.
0

107
116


Somayeh
Shahraki
Department of Mathematics, University of Sistan and Baluchestan, Zahedan, Iran.
Iran
somayehshahraki@yahoo.com


Alireza
Ahmadi Ledari
Department of Mathematics, University of Sistan and Baluchestan, Zahedan, Iran.
Iran
ahmadi.ledar@gmail.com
Banach spaces
Nowhere dual Schur property
Hereditarily $ell_p(c_0)$ Banach spaces
[[1] P. Azimi and J. Hagler, Examples of hereditarily $ell_1$ Banach spaces failing the Schur property, Pacific J. of Math., 122 (1986), pp. 287297.##[2] P. Azimi and A.A. Ledari, A class of Banach sequence spaces analogous to the space of Popov, Czech. Math. J., 59 (2009), pp. 573582.##[3] J. Bourgain, $ell_1$subspace of Banach spaces, Lecture notes, Free University of Brussels.##[4] A.A. Ledari, A class of hereditarily $ell_p$ Banach spaces without Schur property, Iranian Journal of Science and Technology, 42 (2018), pp. 14.##[5] J. Lindenstrauss and L. Tzafriri, Classical Banach spaces. I. Sequence spaces, Springer Verlag, Berlin, 1977.##[6] S.M. Moshtaghioun, Nowhere Schur property in some Operator spaces, Int. Journal of Math. Analysis, 4 (2010), pp. 19291936.##[7] M.M. Popov, A hereditarily $ell_1$ subspace of $L_1$ without the Schur property, Proc. Amer. Math. Soc., 133 (2005), pp. 20232028.##[8] M.M. Popov, More examples of hereditarily $ell_{p}$ Banach spaces, Ukrainian Math. Bull., 2 (2005), pp. 95111.##]
1

Some Observations on Dirac MeasurePreserving Transformations and their Results
https://scma.maragheh.ac.ir/article_34485.html
10.22130/scma.2018.61771.226
1
Dirac measure is an important measure in many related branches to mathematics. The current paper characterizes measurepreserving transformations between two Dirac measure spaces or a Dirac measure space and a probability measure space. Also, it studies isomorphic Dirac measure spaces, equivalence Dirac measure algebras, and conjugate of Dirac measure spaces. The equivalence classes of a Dirac measure space and its measure algebras are presented. Then all of measure spaces that are isomorphic with a Dirac measure space are characterized and the concept of a Dirac measure class is introduced and its elements are characterized. More precisely, it is shown that every absolutely continuous measure with respect to a Dirac measure belongs to the Dirac measure class. Finally, the relation between Dirac measure preserving transformations and strongmixing is studied.
0

117
126


Azadeh
Alijani
ValieAsr University of Rafsanjan, Department of Mathematics, P. O. Box 7713936417, Rafsanjan, Iran.
Iran
alijani@vru.ac.ir


Zohreh
Nazari
ValieAsr University of Rafsanjan, Department of Mathematics, P. O. Box 7713936417, Rafsanjan, Iran.
Iran
znazarirobati@gmail.com
Dirac measure
Measure algebra
Measurepreserving transformation
[[1] G.D. Birkhoff, Proof of the ergodic theorem, Proc. Natl. Acad. Sci. USA., 17 (1931), pp. 656660.##[2] R. Bracewell, The Fourier Transform and Its Applications, McGrawHill, (1986).##[3] P. Dirac, The Principles of Quantum Mechanics, Oxford at the Clarendon Press, (1958).##[4] I.M. Gelfand and G. Shilov, Generalized Functions, Academic Press, (19661968).##[5] E. Hopf, On the time average in dynamics, Proc. Nati. Acad. Sci. USA., 18 (1932), pp. 93100.##[6] G.W. Mackey, Ergodic theory and its signiificance for statistical mechanics and probability theory, Adv. Math., 12 (1974), pp. 178268.##[7] J.C. Maxwell, On Boltzmann's theorem on the average distribution of energy in a system of material points, Trans. Camb. Phil. Soc., 12 (1879), pp. 547575.##[8] K. Peter, Lectures on Ergodic Theory, Springer, (1997).##[9] O. Sarig, Lecture Notes on Ergodic Theory, Springer, (2008).##[10] L. Schwartz, Theorie Des Distributions, Hermann, (1950).##[11] Y.G. Sinai, Dynamical systems II. Ergodic theory with applications to dynamical systems and statistical mechnics, Springer, (1989).##[12] A.M. Vershik, Asymptotic Combinatorics with Applications to Mathematical Physics, Springer, (2003).##[13] J.W. Von Neumann, Proof of the quasiergodic hypothesis, Proc. Nati. Acad. Sci. USA., 18 (1932), pp. 7082.##[14] P. Walters, An Introduction to Ergodic Theory, Springer, (1982).##[15] E. Zeidler, Quantum Field Theory: Basic in Mathematics and Physics, Springer, (2007).##]
1

A FullNT Step Infeasible InteriorPoint Algorithm for Mixed Symmetric Cone LCPs
https://scma.maragheh.ac.ir/article_34483.html
10.22130/scma.2018.67206.260
1
An infeasible interiorpoint algorithm for mixed symmetric cone linear complementarity problems is proposed. Using the machinery of Euclidean Jordan algebras and NesterovTodd search direction, the convergence analysis of the algorithm is shown and proved. Moreover, we obtain a polynomial time complexity bound which matches the currently best known iteration bound for infeasible interiorpoint methods.
0

127
146


Ali
Nakhaei Amroudi
Department of Mathematics and Statistics, Imam Hossein Comprehensive University, Tehran, Iran.
Iran
kpnakhaei@ihu.ac.ir


Ali Reza
Shojaeifard
Department of Mathematics and Statistics, Imam Hossein Comprehensive University,
Tehran, Iran.
Iran
ashojaeifard@ihu.ac.ir


Mojtaba
Pirhaji
Department of Mathematics and Statistics, Imam Hossein Comprehensive University,
Tehran, Iran.
Iran
mojtabapirhaji@yahoo.com
Mixed linear complementarity problem
Symmetric cone
Interiorpoint methods
Polynomial complexity
[[1] M. Achache, Complexity analysis and numerical implementation of a shortstep primaldual algorithm for linear complementarity problems, Appl. Math. Comput., 216 (2010), pp. 18891895.##[2] M. Achache and R. Khebchache, A fullNewton step feasible weighted primaldual interiorpoint algorithm for monotone LCP, Afr. Mat., 26 (2015), pp. 139151.##[3] J. Faraut and A. Koranyi, Analysis on symmetric cones, Oxford University Press, New York, 1994.##[4] L. Faybusovich, Euclidean Jordan algebras and interiorpoint algorithms, Positivity, 1 (1997), pp. 331357.##[5] R.A. Horn and C.R. Johnson, Matrix Analysis, Cambridge University Press, Cambridge 1986.##[6] M. Kojima, N. Megiddo, T. Noma, and A. Yoshise, A unified approach to interior point algorithms for linear complementarity problems, in: Lecture Notes in Computer Science, vol. 538, SpringerVerlag, Berlin, Germany 1991.##[7] Y. Lin and A. Yoshise, A homogeneous model for mixed complementarity problems over symmetric cones, Vietnam J. Math., 35 (2007), pp. 541561.##[8] H. Masouri and M. Pirhaji, A polynomial interiorpoint algorithm for monotone linear complementarity problems, J. Optim. Theory Appl., 157 (2013), pp. 451461.##[9] H. Masouri, M. Zangiabadi, and M. Pirhaji, A full Newton step $O(n)$ infeasibleinteriorpoint algorithm for linear complementarity problems, Nonlinear Anal., Real World Appl., 12 (2011), pp. 454561.##[10] H. Masouri, M. Zangiabadi, and M. Pirhaji, A pathfollowing feasible interiorpoint algorithm for mixed symmetric cone linear complementarity problems, Journal of New Researches in Mathematics, 1 (2016), pp. 109120.##[11] S.H. Schmieta and F. Alizadeh, Extension of primal dual interiorpoint algorithms to symmetric cones, Math. Program. Ser. A, 96 (2003), pp. 409438.##[12] J.F. Sturm, Similarity and other spectral relations for symmetric cones, Linear Algebra Appl. 312 (2000), pp. 135154.##[13] G.Q. Wang, Y. Yue, and X.Z. Ci, Weighthedpathfollowing interiorpoint algorithm to monotone mixed linear complementarity problem, Fuzzy Inf. Eng., 4 (2009), pp. 435445.##[14] M. Zangiabadi, G. Gu, and C. Roos, A full Nesterov Todd step infeasible interiorpoint method for secondorder cone optimization, J. Optim. Theory. Appl., 158 (2013), pp. 816858.##]
1

Some Results on Polynomial Numerical Hulls of Perturbed Matrices
https://scma.maragheh.ac.ir/article_34868.html
10.22130/scma.2018.80849.388
1
In this paper, the behavior of the pseudopolynomial numerical hull of a square complex matrix with respect to structured perturbations and its radius is investigated.
0

147
158


Madjid
Khakshour
Department of Applied Mathematics, Faculty of New Science and Technology, Graduate University of Advanced Technology of Kerman, Kerman, Iran.
Iran
m.khakshour@student.kgut.ac.ir


Gholamreza
Aghamollaei
Department of Pure Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, Iran.
Iran
aghamollaei@uk.ac.ir
Polynomial numerical hull
numerical range
Numerical radius
Perturbation
[[1] E.S. Benilov, Explosive instability in a linear system with neutrally stable eigenmodes, Part 2, Multidimensional disturbances, J. Fluid Mech., 501 (2004), pp. 105124.##[2] A. Greenbaum, Generalizations of the field of values in the study of polynomial functions of a matrix, Linear Algebra Appl., 347 (2002), pp. 233249.##[3] R.A. Horn and C.R. Johnson, Topics in Matrix Analysis, Cambridge University Press, New York, 1991.##[4] M. Khakshour, Gh. Aghamollaei and A. Sheikhhosseini, Field of values of perturbed matrices and quantum states, Turkish J. Math., 42 (2018), pp. 647655.##[5] G. Krishna Kumar and S.H. Lui, On some properties of the pseudospectral radius, Electronic J. Linear Algebra, 27 (2014), pp. 342353.##[6] S.M. Rump, Eigenvalues, pseudospectrum and structured perturbations, Linear Algebra Appl., 413 (2006), pp. 567593.##[7] L.N. Trefethen and M. Embree, Spectra and Pseudospectra: The Behavior of Nonnormal Matrices and Operators, Princeton University Press, Princeton, 2005.##]
1

On the Structure of Metriclike Spaces
https://scma.maragheh.ac.ir/article_34895.html
10.22130/scma.2018.74393.316
1
The main purpose of this paper is to introduce several concepts of the metriclike spaces. For instance, we define concepts such as equallike points, cluster points and completely separate points. Furthermore, this paper is an attempt to present compatibility definitions for the distance between a point and a subset of a metriclike space and also for the distance between two subsets of a metriclike space. In this study, we define the diameter of a subset of a metriclike space, and then we provide a definition for bounded subsets of a metriclike space. In line with the aforementioned issues, various examples are provided to better understand this space.
0

159
171


Amin
Hosseini
Department of Mathematics, Kashmar Higher Education Institute, Kashmar, Iran.
Iran
hosseini.amin82@gmail.com


Ajda
Fosner
University of Primorska, Cankarjeva 5, SI6000 Koper, Slovenia.
Iran
ajda.fosner@fmkp.si
Metriclike space
Partial metric space
Metric space
Equallike points
Completely separate points
[[1] I. Altun, F. Sola, and H. Simsek, Generalized contractions on partial metric spaces, Topol. Appl., 157 (2010), pp. 27782785.##[2] A. AminiHarandi, Metriclike spaces, partial metric spaces and fixed points, Fixed Point Theory Appl., 204 (2012), pp. 210.##[3] M. Bukatin, R. Kopperman, S. G. Matthews, and H. Pajoohesh, Partial metric spaces, Am. Math. Mon., 116 (2009), pp. 708718.##[4] M.M. Deza and Elena Deza, Encyclopedia of distances, Springer, Berlin, 2009.##[5] E. Karapinar and IM. Erha, Fixed point theorems for operators on partial metric spaces, Appl. Math. Lett., 24 (2011), pp. 18941899.##[6] S.G. Matthews, Partial metric topology, in: Proc. 8th Summer Conference on General Topology and Applications, Annals of the New York Academy of Sciences, 728 (1994), pp. 183197.##[7] S.J. O'Neill, Partial metrics, valuations and domain theory, in: Proc. 11th Summer Conference on General Topology and Applications, Annals of the New York Academy of Sciences, 806 (1996), pp. 304315.##]
1

A New Model for the Secondary Goal in DEA
https://scma.maragheh.ac.ir/article_34893.html
10.22130/scma.2018.74414.315
1
The purpose of the current paper is to propose a new model for the secondary goal in DEA by introducing secondary objective function. The proposed new model minimizes the average of the absolute deviations of data points from their median. Similar problem is studied in a related model by Liang et al. (2008), which minimizes the average of the absolute deviations of data points from their mean. By using two well known data sets, which are also used by Liang et al.(2008), and Greene (1990) we compare the results of the proposed new model and several other models.
0

173
183


Harun
Kinaci
Erciyes University, Faculty of Economics and Administrative Sciences, Business Department, Kayseri, Turkey.
Iran
hkinaci@erciyes.edu.tr


Vadoud
Najjari
Young Researchers and Elite Club, Maragheh branch, Islamic Azad University, Maragheh, Iran.
Iran
fnajjary@yahoo.com
Data Envelopment Analysis
Crossefficiency
Linear Programming
Secondary goal
[[1] I. Alp, Performance of evaluation of Goalkeepers of World Cup, G.U. Journal of Science, 19 (2006), pp. 119125.##[2] I. Alp and A. Sozen, Efficiency Assessment of Turkey's Carbonization Index, Energy Sources, Part A: Recovery, Utilization, and Environmental Effects, 33 (2011), pp. 16781691.##[3] T.R. Anderson, K.B. Hollingsworth, and L.B. Inman, The fixed weighting nature of a crossevaluation model, J. of Prod. Anal., 18 (2002), pp. 249255.##[4] T. Anderson and G. Sharp, A New Measure of Baseball Batters Using DEA, Ann. of Oper. Res., 73 (1997), pp. 141155.##[5] J. Doyle and R. Green, Efficiency and cross efficiency in DEA: Derivations, meanings and the uses, J. of the Oper. Res. Soc., 45 (1994), pp. 567578.##[6] W. Greene, A Gammadistributed Stochastic Frontier Model, Journal of Econometrics, J. of Econ., 46 (1990), pp. 141163.##[7] L. Liang, J. Wu, W.D. Cook, and J.Zhu, Alternative secondary goals in DEA crossefficiency evaluation, Int. J. Prod. Econ., 113 (2008), pp. 10251030.##[8] R. Lin, Z. Chen, and W. Xiong, An Iterative Method for Determining Weights in Cross Efficiency Evaluation, Comp. and Ind. Engineering, 101 (2016), pp. 91102.##[9] M. Mercan, A. Reisman, R. Yoalan, and A.B. Emel, The Effect of Scale and Mode of Ownership on the Financial Performance of the Turkish Banking Sector: Results of A DEA Based Analysis, Soc.Econ. Plan. Sciences, 37 (2003), pp. 185202.##[10] H.H. Orkcu and H. Bal, Goal Programming Approaches for Data Envelopment Analysis CrossEfficiency Evaluation, Applied Math. and Comp., 218 (2011), pp. 346356.##[11] G. Tohidi, M. Khodadadi, and E. Rostamian, Improving the Selection Symmetric Weights as a Secondary Goal in DEA CrossEfficiency Evaluation, Int. J. of Math. Modelling and Computations, 3 (2013), pp. 149155.##[12] M.D. Troutt, Derivation of the maximin efficiency ratio model from the maximum decisional efficiency principle, Ann. of Oper. Research, 73 (1997), pp. 323338.##[13] T.R. Sexton, The methodology of data envelopment analysis, In Silkman, R.H. (Ed.) Measuring efficiency: An assessment of Data Envelopment Analysis, San Francisco: JosseyBass, (1986), pp. 729.##[14] A. Sozen and I. Alp, and A. Ozdemir, Assessment Of Operational And Environmental Performance Of The Thermal Power Plants In Turkey By Using Data Envelopment Analysis, E. Policy (Soc. A), 38 (2010), pp. 61946203.##[15] Y.M. Wang and K.S. Chin, Some alternative models for DEA crossefficiency evaluation, Int. J. of Prod. Econ., 128 (2010a), pp. 332338.##[16] Y.M. Wang and K.S. Chin, A neutral DEA model for crossefficiency evaluation and its extension, Expert Sys. with App., 37 (2010b), pp. 36663675.##[17] J. Wu, J. Chu, J. Sun, Q. Z, and L. Liang, Extended Secondary Goal Models for Weights Selection in DEA CrossEfficiency Evaluation, Comp. and Ind. Engineering, 93 (2016), pp. 143151.##[18] J. Zhu, Data envelopment analysis vs. principal component analysis: An illustrative study of economic performance of Chinese cities, E. J. of Oper. Res., 111 (1998), pp. 5061.##]
1

Inverse Problem for Interior Spectral Data of the Dirac Operator with Discontinuous Conditions
https://scma.maragheh.ac.ir/article_32917.html
10.22130/scma.2018.85988.457
1
In this paper, we study the inverse problem for Dirac differential operators with discontinuity conditions in a compact interval. It is shown that the potential functions can be uniquely determined by the value of the potential on some interval and parts of two sets of eigenvalues. Also, it is shown that the potential function can be uniquely determined by a part of a set of values of eigenfunctions at an interior point and parts of one or two sets of eigenvalues.
0

185
197


Mohammad
Shahriari
Department of Mathematics, Faculty of Science, University of Maragheh, P.O. Box 55136553, Maragheh, Iran.
Iran
shahriari@maragheh.ac.ir


Reza
Akbari
Department of Mathematical Sciences, Payame Noor University, Iran.
Iran
r9reza@yahoo.com


Mostafa
Fallahi
Department of Mathematics, Faculty of Science, University of Maragheh, P.O. Box 55136553, Maragheh, Iran.
Iran
fallahi1mostafa@yahoo.com
Dirac operator
Inverse spectral theory
Discontinuous conditions
[[1] R.Kh. Amirov, On SturmLiouville operators with discontinuity conditions inside an interval, J. Math. Anal. Appl., 317 (2006), pp. 163176.##[2] R.Kh. Amirov, On system of Dirac differential equations with discontinuity conditions inside an interval, Ukrainian Math. J., 57 (2005), pp. 712727.##[3] G. Freiling and V.A. Yurko, Inverse SturmLiouville problems and their applications, NOVA Science Publishers, New Yurk, 2001.##[4] M.G. Gasymov and B.M. Levitan, The inverse problem for a Dirac system, Dokl. Akad. Nauk SSSR, 167 (1966), pp. 967970.##[5] Y. Guo, G. Wei, and R. Yao, Inverse problem for interior spectral data of discontinuous Dirac operator, Appl. Math. Comput., 268 (2015), pp. 775782.##[6] O. Hald, Discontinuous inverse eigenvalue problem, Commun. Pure. Appl. Math., 37 (1984), pp. 539577.##[7] H. Hochstadt and B. Lieberman, An inverse SturmLiouville problem with mixed given data, SIAM J. Appl. Math., 34 (1978), pp. 676680.##[8] M. Kobayashi, A uniqueness proof for discontinuous inverse SturmLiouville problems with symmetric potentials, Inverse Probl., 5 (1989), pp. 767781.##[9] B.J. Levin, Distribution of zeros of entire functions, AMS. Transl. Vol. 5, Providence, 1964.##[10] B.Ya. Levin, Entire functions, MGU, Moscow, 1971.##[11] B.M. Levitan and I.S. Sargsjan, SturmLiouville and Dirac operators, Kluwer Academic Publishers, Dodrecht, Boston, London, 1991.##[12] K. Mochizuki and I. Trooshin, Inverse problem for interior spectral data of the Dirac operator, Comm. Korean Math. Soc., 16 (2001), pp. 437442.##[13] K. Mochizuki and I. Trooshin, Inverse problem for interior spectral data of SturmLiouville operator, J. Inverse Illposed Probl., 9 (2001), pp. 425433.##[14] K. Mochizuki and I. Trooshin, Inverse problem for interior spectral data of the Dirac operator on a finite interval, Publ. RIMS, KyotoUniv., 38 (2002), pp. 387395.##[15] M. Shahriari, A.J. Akbarfam, and G. Teschl, Uniqueness for inverse SturmLiouville problems with a finite number of transmission conditions, J. Math. Anal. Appl., 395 (2012), pp. 1929.##[16] Z. Wei, Y. Guo, and G. Wei, Incomplete inverse spectral and nodal problems for Dirac operator, Adv. Difference Equ., 2015 (2015), 188.##[17] C. Willis, Inverse SturmLiouville problems with two discontinuities, Inverse Probl., 1 (1985), pp. 263289.##[18] C.F. Yang, HochstadtLieberman theorem for Dirac operator with eigenparameter dependent boundary conditions, Nonlinear Anal., 74 (2011), pp. 24752484.##[19] V. Yurko, Integral transforms connected with discontinuous boundary value problems, Int. Trans. Spec. Functions, 10 (2000), pp. 141164.##]
1

A Subclass of Analytic Functions Associated with Hypergeometric Functions
https://scma.maragheh.ac.ir/article_34484.html
10.22130/scma.2018.72370.290
1
In the present paper, we have established sufficient conditions for Gaussian hypergeometric functions to be in certain subclass of analytic univalent functions in the unit disc $mathcal{U}$. Furthermore, we investigate several mapping properties of Hohlov linear operator for this subclass and also examined an integral operator acting on hypergeometric functions.
0

199
210


Santosh B.
Joshi
Department of Mathematics, Walchand College of Engineering, Sangli 416415, India.
Iran
joshisb@hotmail.com


Haridas H.
Pawar
Department of Mathematics, Sveri's College of Engineering, Pandharpur 413304, India.
Iran
haridas_pawar007@yahoo.co.in


Teodor
Bulboaca
Faculty of Mathematics and Computer Science, Babec{s}Bolyai University, 400084 ClujNapoca, Romania.
Iran
bulboaca@math.ubbcluj.ro
Univalent function
Starlike and convex functions
Gaussian hypergeometric function
CarlsonShaffer operator
Coefficient estimates
[[1] M.K. Aouf, A.O. Mostafa, and H.M. Zayed, Some constraints of hypergeometric functions belong to certain subclasses of analytic functions, J. Egyptian Math. Soc., 24 (2016), pp. 16.##[2] B.C. Carlson and D.B. Shaffer, Starlike and prestarlike hypergeometric functions, J. Math. Anal. Appl., 15 (1984), pp. 737745.##[3] P.L. Duren, Univalent functions, SpringerVerlag, New York, 1983.##[4] J. Dziok and H.M. Srivastava, Certain subclasses of analytic functions associated with the generalized hypergeometric function, Integral Transforms Spec. Funct., 14 (2003), pp. 718.##[5] J. Dziok and H.M. Srivastava, Classes of analytic functions associated with the generalized hypergeometric function, App. Math. Comput., 103 (1999), pp. 113.##[6] Y.E. Hohlov, Operators and operations in the class of univalent functions, Izv. Vyss. Ucebn. Zaved. Mat. (in Russian), 10 (1978) 8389.##[7] S.S. Joshi, A certain subclass of analytic functions associated with fractional derivative operator, Tamsui Oxf. J. Inf. Math. Sci., 24 (2008), pp. 201214.##[8] S. Kanas and H.M. Srivastava, Linear operators associated with kuniformly convex functions, Integral Transforms Spec. Funct., 9 (2000), pp. 121132.##[9] J.A. Kim and K.H. Shon, Certain properties for convolutions involving hypergeometric functions, Int. J. Math. Math. Sci., 17 (2003), pp. 10831091.##[10] S.R. Kulkarni, Some problems connected with univalent functions, Ph.D. Thesis. Shivaji University, Kolhapur, 1981.##[11] E. Merkes and B.T. Scott, Starlike hypergeometric functions, Proc. Amer. Math. Soc., 12 (1961), pp. 885888.##[12] M.S. Robertson, On the theory of univalent functions, Ann. Math., 37 (1936), pp. 374408.##[13] S. Ruscheweyh and V. Singh, On the order of starlikeness of hypergeometric functions, J. Math. Anal. Appl., 113 (1986), pp. 111.##[14] N. Shukla and P. Shukla, Mapping properties of analytic function defined by hypergeometric functions, Soochow J. Math., 25 (1999), pp. 1936.##[15] H. Silverman, Starlike and convexity properties for hypergeometric functions, J. Math. Anal. Appl., 172 (1993), pp. 574581.##[16] H.M. Srivastava, Some foxwright generalized hypergeometric functions and associated families of convolution operators, Appl. Anal. Discrete Math., 1 (2007), pp. 5671.##[17] H.M. Srivastava and S. Owa (eds.), Current topics in analytic function theory, World Sci. Publ., 1992.##[18] H. Tang and G.T. Deng, Subordination and superordination preserving properties for a family of integral operators involving the noor integral operator, J. Egyptian Math. Soc., 22 (2014), pp. 352361.##]