A Comprehensive Subclass of Bi-Univalent Functions Associated with Chebyshev Polynomials of the Second Kind

TL;DR

This paper introduces a new subclass of bi-univalent functions linked to Chebyshev polynomials of the second kind, deriving coefficient bounds and inequalities, and relating to existing results.

Contribution

It presents a novel subclass of bi-univalent functions associated with Chebyshev polynomials and establishes bounds and inequalities for this class.

Findings

Upper bounds for second and third Taylor coefficients

Fekete-Szego inequalities for the subclass

Connections to previously known results

Abstract

Our objective in this paper is to introduce and investigate a newly-constructed subclass of normalized analytic and bi-univalent functions by means of the Chebyshev polynomials of the second kind. Upper bounds for the second and third Taylor-Maclaurin coefficients, and also Fekete-Szego inequalities of functions belonging to this subclass are founded. Several connections to some of the earlier known results are also pointed out.