Fekete–Szegö problem for a general subclass of analytic functions
Fekete–Szegö problem for a general subclass of analytic functions
In this present investigation, we introduced a certain subclass of starlike and convex functions of complexorder b , using a linear multiplier differential operator $D_{gamma,mu}^m;f(z)$ For this class, the Fekete–Szegö problem is completelysolved. Various new special cases are considered.
___
- [1] Abdel-Gawad HR, Thomas DK. The Fekete Szegö problem for strongly close-to-convex functions. Proceeding of
the American Mathematical Society 1992; 114: 345-349.
- [2] Al-Oboudi FM. On univalent functions defined by a generalized Salagean operator. International Journal of Mathematics
and Mathematical Sciences 2004; 27: 1429-1436.
- [3] Chonweerayoot A, Thomas DK, Upakarnitikaset W. On the Fekete Szegö theorem for close-to-convex functions.
Publications de I’Institut Mathėmatique (Beograd) (N.S.) 1992; 66: 18-26.
- [4] Darus M, Thomas DK. On the Fekete Szegö theorem for close-to-convex functions. Mathematica Japonica 1996;
44: 507-511.
- [5] Darus M, Thomas DK. On the Fekete Szegö theorem for close-to-convex functions. Mathematica Japonica 1998;
47: 125-132.
- [6] Deniz E, Orhan H. The Fekete Szegö problem for a generalized subclass of analytic functions. Kyungpook Mathematical
Journal 2010; 50: 37-47.
- [7] Fekete M, Szegö G. Eine Bemerkung über ungerade schlichte Funktionen. Journal of the London Mathematical
Society 1933; 8: 85-89 (in German).
- [8] Kanas S, Darwish HE. Fekete Szegö problem for starlike and convex functions of complex order. Applied Mathematics
Letters 2010; 23 (7): 777-782.
- [9] Keogh FR, Merkes EP. A coefficient inequality for certain classes of analytic functions. Proceedings of the American
Mathematical Society 1969; 20: 8-12.
- [10] Koepf W. On the Fekete Szegö problem for close-to-convex functions. Proceedings of the American Mathematical
Society 1987; 101: 89-95.
- [11] London RR. Fekete Szegö inequalities for close-to-convex functions. Proceedings of the American Mathematical
Society 1993; 117: 947-950.
- [12] Ma W, Minda D. A unified treatment of some special classes of univalent functions. In: Proceeding of Conference
on Complex Analytic 1994; 157-169.
- [13] Nasr MA, Aouf MK. Starlike function of complex order. Journal of Natural Science Mathematics 1985; 25: 1-12.
- [14] Nasr MA, Aouf MK. On convex functions of complex order. Mansoura Science Bulletin 1982; 565-582.
- [15] Orhan H, Deniz E, Rãducanu D. The Fekete–Szegö problem for subclasses of analytic functions defined by a
differential operator related to conic domains. Computer and Mathematics with Application 2010; 59: 283-295.
- [16] Orhan H, Rãducanu D. Fekete–Szegö problem for strongly starlike functions associated with generalized hypergeometric
functions. Mathematical and Computer Modelling 2009; 50: 430-438.
- [17] Orhan H, Deniz E, Çağlar M. Fekete–Szegö problem for certain subclasses of analytic functions. Demonstratio
Mathematica 2012; 45 (4): 835-846.
- [18] Pfluger A. The Fekete–Szegö inequality by a variational method. Annales Academiae Scientiorum. Fennicae Seria
AI 1984; 10.
- [19] Pommerenke C. Univalent functions. In: Studia Mathematica Mathematische Lehrbucher, Vandenhoeck and
Ruprecht, 1975
- [20] Rãducanu D, Orhan H. Subclasses of analytic functions defined by a generalized differential operator. International
Journal of Mathematical Analysis 2010; 4 (1): 1-15.
- [21] Sãlãgean GS. Subclasses of univalent functions, complex analysis. In: Proceedings of the 5th Romanian-Finnish
Seminar, Bucharest 1983; 1013: 362-372.
- [22] Wiatrowski P. The coefficients of a certain family of holomorphic functions. Zeszyty Naukowe Uniwersyteta
Lodzkiego, Nauki Matematyczno Przyrodnicze Seria II 1971; 75-85.