• 2026-06-17
• Olatunji S.O, Awolere I.T, Gbolagade A. M.
• Volume 8, Issue 1

Abstract

Geometric Function Theory (GFT), an important area of complex analysis, continues to attract considerable attention due to its wide range of applications in mathematics and related scientific disciplines. In this paper, we investigate subclasses of q-bi-Sakaguchi functions defined in connection with the generalized distribution series and Bernoulli polynomials. By utilizing the analytical properties of Bernoulli polynomials within the framework of the generalized distribution series, we derive bounds for the initial Taylor-Maclaurin coefficients of two newly introduced subclasses of these functions. Furthermore, the obtained coefficient estimates are employed to establish the corresponding Fekete-Szegő inequalities. The approach adopted in this work provides a systematic technique for studying coefficient problems associated with q-bi-univalent function classes. The results obtained generalize and extend several earlier findings in the literature and further enrich the theory of analytic and bi-univalent functions within the framework of Geometric Function Theory. The novelty of this study lies in introducing the combined use of generalized distribution series and Bernoulli polynomial techniques in the analysis of q-bi-Sakaguchi functions, leading to new coefficient bounds and Fekete-Szego type results for newly defined subclasses.