Maclaurin Coefficient Estimates of Bi-Univalent Functions Connected with the q-Derivative

Abstract

In this paper we introduce a new subclass of the bi-univalent functions defined in the open unit disc and connected with a q-analogue derivative. We find estimates for the first two Taylor-Maclaurin coefficients a 2 and a 3 for functions in this subclass, and we obtain an estimation for the Fekete-Szegő problem for this function class.

Keywords

• bi-univalent functions
• hadamard (convolution) product
• coefficients bounds
• <i>q</i>-derivative operator
• differential subordination