Applications of q-Calculus in Coefficient Problems for Normalized and Bi-Univalent Function Classes

In this work, we introduce a distinguished subclass of analytic functions whose structure is based on q-calculus, providing a generalization of several well-known classes previously studied in the literature. This subclass represents one of the notable applications of fractional calculus within geometric function theory and the coefficient problems of analytic functions. The main contribution of our study lies in establishing sharp or near-optimal upper bounds for several significant problems, despite the presence of the parameter q, achieved through novel and effective proof techniques.

کلیدواژه ها:

q-Calculus ، Analytic functions ، Univalent and bi-univalent function classes ، Coefficient estimates ، Fekete--Szegö problem ، Hankel determinants