COEFFICIENT BOUNDS FOR REGULAR AND BI-UNIVALENT FUNCTIONS LINKED WITH GEGENBAUER POLYNOMIALS

Abstract

The main goal of the paper is to initiate and explore two sets of regular and bi-univalent (or bi-Schlicht) functions in 𝔇 = {𝑧 ∈ C : |𝑧| < 1} linked with Gegenbauer polynomials. We investigate certain coefficient bounds for functions in these families. Continuing the study on the initial coefficients of these families, we obtain the functional of Fekete-Szegö for each of the two families. Furthermore, we present few interesting observations of the results investigated.

Keywords

• fekete-szeg¨o functional
• regular function
• bi-univalent function
• gegenbauer polynomials