Coefficient Estimate and Fekete-Szeg\"{o} Problems for Certain New Subclasses of Bi-univalent Functions Defined by Generalized Bivariate Fibonacci Polynomial

Abstract

This article deals with two new subclasses of analytic and bi-univalent functions in the open unit disk, which is defined by applying subordination principle between analytic functions and the generalized Bivariate Fibonacci polynomials. Bounds for coefficients $\left|a_{2}\right|$ and $\left|a_{3}\right|$ of functions in these subclasses are estimated in terms of generalized Bivariate Fibonacci polynomials. In addition, the Fekete-Szeg\"{o} problem is handled for the members of these subclasses and several consequences and examples of the main results are presented. The results of article generalize some of the previously published papers in the literature.

Keywords

• bi-univalent function
• coefficient estimates
• fekete-szeg\"{o} functional
• bivariate fibonacci polynomials