Applications of q-Borel distribution series involving q-Gegenbauer polynomials to subclasses of bi-univalent functions

Abstract

This study introduces a new class of bi-univalent functions in the open disk using q-Borel distribution series and q-Gegenbauer polynomials. It provides estimates for the Taylor coefficients |μ2| and |μ3| for this family of functions, as well as solutions for the Fekete-Szegö functional problems associated with this subclass. The study presents various innovative findings that result from the unique parameters used in the main results.

Keywords

• q-Borel distribution series
• Subordination
• q-Gegenbauer polynomials
• q-calculus
• Fekete-Szegö problem
• Bi-u