TY - JOUR TT - On The Fekete-Szegö Problem for Generalized Class Mα,γ(β) Defined By Differential Operator AU - Sakar, Fethiye Müge AU - Aytaş, Sultan AU - Güney, Hatun Özlem PY - 2016 DA - December DO - 10.19113/sdufbed.12069 JF - Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi JO - J. Nat. Appl. Sci. PB - Süleyman Demirel Üniversitesi WT - DergiPark SN - 1308-6529 SP - 456 EP - 459 VL - 20 IS - 3 KW - Univalent functions KW - Analytic; Starlike; Convex; Fekete-Szegö problem N2 - In this study the classical Fekete-Szegö problem was investigated. Given f(z)=z+a2z2+a3z3+... to be an analytic standartly normalized function in the open unit disk U={z ∈ C : |z|<1}. For |a3-μa22|, a sharp maximum value is provided through the classes of S*α,γ(β) order β and type α under the condition of μ≥1. CR - [1] Fekete-Szegö, M. 1933. Eine Bemerkung uber ungrade schlicht funktionen. J. London Math. Soc., 8, 85-89 (in German). CR - [2] Choonweerayoot, A., Thomas, D.K. Upakarnitikaset, W. 1991. On the coefficients of close-to convex functions. Math. Japon, 36 (5),819–826. CR - [3] Keogh, F.R., Merkes, E.P. 1969. A coefficient inequality for certain classes of analytic functions.Proc. Am. Math. Soc.,20,8–12 . CR - [4] Srivastava, H.M., Mıshra, A.K., Das, M.K. 2000. The Fekete-Szegö problem for a subclass of close-to convex function.Complex Variables,44,145–163. CR - [5] Abdel-Gawad, H.R., Thomas, D.K. 1991. A subclass of close-to convex functions. Publ. Inst. Math. (Beograd) (NS),49 (63), 61–66. CR - [6] Abdel-Gawad, H.R., Thomas, D.K. 1992. The Fekete-Szegö problem for strongly close-to convex functions.Proc.Am. Math. Soc.,114 (2),345–349 . CR - [7] Nasr, M.A., El-Gawad, H.R. 1991. On the Fekete-Szegö problem for close-to convex functions of order ρ. In: New Trends in Geometric Function Theory and Applications (Madras 1990), World Science Publishing, River Edge, NJ, 66–74. CR - [8] Darus, M., Thomas, D.K. 1996. On the Fekete-Szegö theorem for close-to convex functions. Math. Japon, 44 (3),507-511. CR - [9] Darus, M., Thomas, D.K. 1998. On the Fekete-Szegö theorem for close-to convex functions. Math. Japon, 47 (1), 125-132. CR - [10] Goel, R.M.,Mehrok, B.S. 1991. A coefficient inequality for certain classes of analytic functions. Tamkang J. Math., 22 (2), 153-163. CR - [11] London, R.R.1993. Fekete-Szegö inequalities for close-to-convex functions. Proc. Am. Math. Soc.,117 (4),947–950. CR - [12] Trimble, S.Y. 1975. A coefficient inequality for convex univalent functions. Proc. Am. Math. Soc.,48, 266–267. CR - [13] Koepf, W. 1987. On the Fekete-Szegö problem for close-to convex functions. II. Arch. Math. (Basel),49 (5), 420–433. CR - [14] Koepf, W. 1987. On the Fekete-Szegö problem for close-to convex functions. Proc. Am. Math. Soc.,101 (1), 89–95. CR - [15] Altınkaya, Ş., Yalçın, S. 2014. Fekete-Szegö Inequalities for Certain Classes of Bi-univalent Functions.International Scholarly Research Notices,Volume, Article ID 327962, 6 pages. CR - [16] Altınkaya, Ş., Yalçın, S. 2014. Fekete-Szegö Inequalities for Classes of Bi-univalent Functions defined by subordination. Advances in Mathematics: Scientific Journal, 3 (2),63-71. CR - [17] Sokół, J.,Raina, R.K., Yilmaz Özgür, N.2015. Applications of k-Fibonacci numbers for the starlike analytic functions.Hacet. J. Math. Stat., 44(1), 121-127. CR - [18] Nalinakshi, L., Parvatham, R. 1995. On Salagean-Pascu Type of Generalised Sakaguchi Class of Functions. Kyungpook Math.J., 35, 1-15. CR - [19] Salagean, G.S. 1981. Subclasses of univalent funtions. Lecture notes in Mathematics Springer Verlag, 1013, 363-372. CR - [20] Kaplan, W. 1952. Close-to convex schlicht functions. Michigan Math. J.,1,169–185. CR - [21] Pommerenke, Ch. 1975. Univalent Functions.With a chapter on quadratic differentials by Gerd Jensen.StudiaMathematica/MathematischeLehrbucher,BandXXV,Vandenheck&Ruprecht. Göttingen, MR 58#22526.Zbl 298.30014. CR - [22] Jahangiri, M.1995. A coefficient inequality for a class of close-to convex functions. Math. Japon, 41 (3), 557-559. CR - [23] Orhan, H., Kamali, M. 2003. On the Fekete-Szegö problem. Applied Mathematics and Computation, 144, 181-186. CR - [24] Frasin, B.A., Darus, M. 2000. On the Fekete-Szegö problem. Internet J. Math. Sci., 24 (9), 577-581. UR - https://doi.org/10.19113/sdufbed.12069 L1 - http://dergipark.org.tr/tr/download/article-file/267019 ER -