# Coefficient bounds for a new family of bi-univalent functions associated with $(U,V)$-Lucas polynomials

Document Type : Research Paper

Authors

1 Department of Mathematics, University of Ilorin, P. M. B. 1515, Ilorin, Nigeria

2 University of Al-Qadisiyah, College of science, Department of Mathematics, Al Diwaniyah, Al-Qadisiyah, Iraq

Abstract

The aim of this paper is to use (U,V)-Lucas polynomials to introduce and study a new family of holomorphic and bi-univalent functions defined in the open unit disk which involve q-derivative operator. We investigate upper bounds for the Taylor-Maclaurin coefficients |d2| and |d3| and Fekete- Szego ̈ problem for functions belongs to this new family. Some interesting consequences of the results established here are indicated.

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