Coefficient bounds for regular and bi-univalent functions linked with Gegenbauer polynomials

Abstract

. Making use of Gegenbauer polynomials, we initiate and explore two sets of normalized regular and bi-univalent (or bi-Schlicht) functions in D = { z ∈ C : | z | < 1 } linked with Gegenbauer polynomials. We investi-gate certain coefficients bounds and the Fekete-Szeg¨o functional for functions in these families. We also present few interesting observations and provide relevant connections of the results investigated.