ON THE FEKETE-SZEG¨O PROBLEM FOR SUBCLASSES OF ANALYTIC FUNCTIONS DEFINED BY LINEAR DERIVATIVE OPERATOR

Abstract

In applying a generalized linear derivative operator Dα,δ(m, q, λ), a new subclass of analytic functions denoted by S α,δ(m, q, λ, φ), is introduced. For this class, sharp bounds for the Fekete- Szeg¨o functional |a3 − µa2 2 | are obtained. Also we give applications of our results to certain functions defined through convolution (or Hadamard product) and in particular, we consider a class of functions defined by fractional derivatives. The aim of this paper is to generalize the Fekete-Szeg¨o inequalities given by Srivastava and Mishra [