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

Awara Ahmed  Ali; Pishtiwan Othman  Sabir

doi:10.24996/ijs.2026.67.9.22

Authors

Awara Ahmed Ali Department of Mathematics, College of Science, University of Sulaimani, Sulaymaniyah 46001, Iraq https://orcid.org/0009-0007-6204-2993
Pishtiwan Othman Sabir Department of Mathematics, College of Science, University of Sulaimani, Sulaymaniyah 46001, Iraq https://orcid.org/0000-0001-9355-3402

DOI:

https://doi.org/10.24996/ijs.2026.67.9.22

Keywords:

Regular function, Schlicht function, Bi-schlicht function, Bazilevič function, Close-to-convex function, Fekete-Szegö inequality

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.