Applications of (M,N)-Lucas Polynomials for Holomorphic and Bi-Univalent Functions

Abstract

In the current investigation, we use the (M,N)-Lucas Polynomials to establish upper bounds for the second and third coefficients of functions belongs to a new family of holomorphic and bi-univalent functions defined in the open unit disk $\mathbb{D}$. Also, we discuss Fekete-Szeg$\ddot{o}$ problem for functions belongs to this family.