Tejas, Nagamangala SathyanandaAltinkaya, Şahsene A.Raju, Dasanur ShivannaMagesh, Nanjundan2026-01-312026-01-312024https://doi.org/10.22080/cjms.2024.27503.1702https://hdl.handle.net/20.500.12662/10579Our 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.eninfo:eu-repo/semantics/closedAccessBazilevi? functionBi-univalent functionFekete-Szegö esti-mateLucas polynomialsArticle10.22080/cjms.2024.27503.17022-s2.0-1050236819363432N/A31113