Fekete-Szegö Functional for -Bazilevič-Type Close-to-Convex Functions

Abstract

     Schlicht function theory is a subfield of complex analysis and falls within the broader scope of geometric function theory, focusing on the relationship between geometric transformations and one-to-one complex-valued functions. Inspired by the promising applications of fractional -calculus, we examine analytic functions in this paper and investigate various subfamilies of regular, schlicht, and bi-schlicht functions based on generalized conditions and fundamental geometric properties such as starlikeness, convexity, and close-to-convexity. Furthermore, we determine bounded values for Fekete-Szegö-type problems. Our findings contribute to the growing structure of research on subfamilies of regular functions, with implications for further studies in the geometric function theory of complex analysis.