Coefficient bounds and Fekete-Szegő inequality for a certain family of holomorphic and bi-univalent functions defined by (M,N)-Lucas polynomials

Abstract

In the current work, we use the (M,N)-Lucas Polynomials to introduce a new family of holomorphic and bi-univalent functions which involve a linear combination between Bazilevic functions and ?-pseudo-starlike function defined in the unit disk D and establish upper bounds for the second and third coefficients of functions belongs to this new family. Also, we discuss Fekete-Szeg? problem in this new family.