Fekete–Szegö Inequality for Bi-Univalent Functions Subordinate to Horadam Polynomials

Abstract

Making use of Horadam polynomials, we propose a special family of regular functions of the type gz=z+∑j=2∞djzj which are bi-univalent (or bi-schlicht) in the disc z∈ℂ:z<1. We find estimates on the coefficients d2 and d3 and the functional of Fekete–Szegö for functions in this subfamily. Relevant connections to existing results and new observations of the main result are also presented.