Initial Lucas Polynomial Coefficient Bounds for Bi-Bazilevi? Functions

Our current investigation is primarily motivated by the application of special polynomials in Geometric Function Theory (GFT). This paper aims to utilize (M, N)-Lucas polynomials to estimate the initial coefficient bounds |a<inf>2</inf>| and |a<inf>3</inf>| for a subclass of bi-univalent functions (Formula presented) consisting of analytic functions normalized by the condition f(0) = f? (0) ? 1 = 0. We then derive the famous Fekete-Szegö inequality estimate. We also establish connections between our results and those examined in previous investigations. © 2024 by University of Mazandaran.