A Generalization of Gegenbauer Polynomials and Bi-Univalent Functions

Abstract

Three subclasses of analytic and bi-univalent functions are introduced through the use of q−Gegenbauer polynomials, which are a generalization of Gegenbauer polynomials. For functions falling within these subclasses, coefficient bounds a2 and a3 as well as Fekete–Szegö inequalities are derived. Specializing the parameters used in our main results leads to a number of new results.

Keywords

• Fekete–Szegö problem
• q–Gegenbauer polynomials
• bi-univalent functions
• q–calculus
• analytic functions