A Bazilevic-type function associated with the class of univalent functions with study Coefficient Bounds and Fekete-Szego inequalities

Background The Fekete–Szegö inequality and coefficient bounds play a fundamental role in the study of Bazilevič-type functions, a subclass of univalent functions with significant applications in complex analysis and related mathematical fields. These functions have been extensively studied for their geometric properties and coefficient behavior, yet there remains a need to explore subclasses defined via differential operators and subordination techniques to obtain sharper and more general bounds. Understanding the coefficient structure of these functions provides insight into their analytic behavior and extends classical results in the theory of univalent functions. Methods This study focuses on a specific subclass of Bazilevič-type functions and investigates its properties using differential subordination and differential operators. These mathematical tools are employed to derive explicit coefficient estimates and establish the Fekete–Szegö inequalities. The analysis involves careful application of operator techniques to obtain bounds that reflect the influence of the subclass parameters on the analytic functions under consideration. Results The derived inequalities demonstrate the effectiveness of differential operators in obtaining precise coefficient constraints. The results highlight how variations in the defining parameters of the subclass influence the function behavior, providing clear and explicit bounds for the coefficients. These findings extend existing results in the literature and offer new insights into the structure of Bazilevič-type functions. Conclusions Overall, this study provides a systematic approach to understanding the coefficient structure of Bazilevič-type functions. The findings establish a foundation for further theoretical research on univalent functions and offer tools that can be applied in both theoretical investigations and practical problems in complex analysis. The results contribute to the broader understanding of analytic functions and their applications in mathematical modeling.