Certain Subclasses of Analytic and Bi-Univalent Functions Governed by the Gegenbauer Polynomials Linked with q-Derivative

Abstract

In this paper, we introduce and investigate two new subclasses of analytic and bi-univalent functions using the q-derivative operator Dq0<q<1 and the Gegenbauer polynomials in a symmetric domain, which is the open unit disc Λ=℘:℘∈Cand℘<1. For these subclasses of analytic and bi-univalent functions, the coefficient estimates and Fekete–Szegö inequalities are solved. Some special cases of the main results are also linked to those in several previous studies. The symmetric nature of quantum calculus itself motivates our investigation of the applications of such quantum (or q-) extensions in this paper.