On The Fekete-Szegö Problem for Generalized Class <i>M</i>α,γ(β) Defined By Differential Operator

Yıl 2016, Cilt: 20 Sayı: 3, 456 - 459, 11.11.2016

Fethiye Müge Sakar Sultan Aytaş Hatun Özlem Güney

https://doi.org/10.19113/sdufbed.12069

https://izlik.org/JA72MA34CC

Öz

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.

Anahtar Kelimeler

Univalent functions , Analytic; Starlike; Convex; Fekete-Szegö problem

Kaynakça

• [1] Fekete-Szegö, M. 1933. Eine Bemerkung uber ungrade schlicht funktionen. J. London Math. Soc., 8, 85-89 (in German).
• [2] Choonweerayoot, A., Thomas, D.K. Upakarnitikaset, W. 1991. On the coefficients of close-to convex functions. Math. Japon, 36 (5),819–826.
• [3] Keogh, F.R., Merkes, E.P. 1969. A coefficient inequality for certain classes of analytic functions.Proc. Am. Math. Soc.,20,8–12 .
• [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.
• [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.
• [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 .
• [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.
• [8] Darus, M., Thomas, D.K. 1996. On the Fekete-Szegö theorem for close-to convex functions. Math. Japon, 44 (3),507-511.
• [9] Darus, M., Thomas, D.K. 1998. On the Fekete-Szegö theorem for close-to convex functions. Math. Japon, 47 (1), 125-132.
• [10] Goel, R.M.,Mehrok, B.S. 1991. A coefficient inequality for certain classes of analytic functions. Tamkang J. Math., 22 (2), 153-163.
• [11] London, R.R.1993. Fekete-Szegö inequalities for close-to-convex functions. Proc. Am. Math. Soc.,117 (4),947–950.
• [12] Trimble, S.Y. 1975. A coefficient inequality for convex univalent functions. Proc. Am. Math. Soc.,48, 266–267.
• [13] Koepf, W. 1987. On the Fekete-Szegö problem for close-to convex functions. II. Arch. Math. (Basel),49 (5), 420–433.
• [14] Koepf, W. 1987. On the Fekete-Szegö problem for close-to convex functions. Proc. Am. Math. Soc.,101 (1), 89–95.
• [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.
• [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.
• [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.
• [18] Nalinakshi, L., Parvatham, R. 1995. On Salagean-Pascu Type of Generalised Sakaguchi Class of Functions. Kyungpook Math.J., 35, 1-15.
• [19] Salagean, G.S. 1981. Subclasses of univalent funtions. Lecture notes in Mathematics Springer Verlag, 1013, 363-372.
• [20] Kaplan, W. 1952. Close-to convex schlicht functions. Michigan Math. J.,1,169–185.
• [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.
• [22] Jahangiri, M.1995. A coefficient inequality for a class of close-to convex functions. Math. Japon, 41 (3), 557-559.
• [23] Orhan, H., Kamali, M. 2003. On the Fekete-Szegö problem. Applied Mathematics and Computation, 144, 181-186.
• [24] Frasin, B.A., Darus, M. 2000. On the Fekete-Szegö problem. Internet J. Math. Sci., 24 (9), 577-581.