On the Fekete-Szegö Problem for a Certain Class of Meromorphic Functions Using q-Derivative Operator

Mohamed Kamal Aouf; Halit Orhan

doi:10.5666/KMJ.2018.58.2.307

Article

Kyungpook Mathematical Journal 2018; 58(2): 307-318

Published online June 23, 2018

On the Fekete-Szegö Problem for a Certain Class of Meromorphic Functions Using q-Derivative Operator

Mohamed Kamal Aouf and Halit Orhan^*

Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt, e-mail: mkaouf127@yahoo.com, Department of Mathematics, Faculty of Science, Ataturk University, Erzurum 25240, Turkey, e-mail: orhanhalit607@gmail.com

Received: October 6, 2017; Accepted: March 29, 2018

Abstract

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Abstract

In this paper, we obtain Fekete-Szegö inequalities for certain class of meromorphic functions f(z) for which -(1-αq)qzDqf(z)+αqzDq [zDqf(z)](1-αq)f(z)+αzDqf(z)≺ϕ(z)(α∈ℂ(0,1], 0<q<1).

Sharp bounds for the Fekete-Szegö functional ∣a1-μa02∣ are obtained.

Keywords: Analytic, meromorphic, q-starlike and convex functions, Fekete-Szegö, problem, convolution