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 is an element of C : vertical bar z vertical bar < 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-Szego for each of the two families. Furthermore, we present few interesting observations of the results investigated.