Applications of (M,N)-Lucas Polynomials for a Certain Family of Bi-Univalent Functions Associating λ-Pseudo-Starlike Functions with Sakaguchi Type Functions

Abstract

In this article, we use the (M,N)-Lucas Polynomials to determinate upper bounds for the Taylor-Maclaurin coefficients $\left|a_{2}\right|$ and $\left| a_{3}\right|$ for functions belongs to a certain family of holomorphic and bi-univalent functions associating $\lambda$-pseudo-starlike functions with Sakaguchi type functions defined in the open unit disk $\mathbb{D}$. Also, we discuss Fekete-Szeg\"{o} problem for functions belongs to this family.