Bounds on Hankel Determinants with Fekete-Szegö Parameter for Bazilević Functions
Year: 2026
Type: article
Abstract: Background: In Geometric Function Theory, a central area of complex analysis, researchers study the geometric properties of analytic and univalent functions in the unit disk. A significant part of this work involves defining some subclasses of functions and investigating their properties, such as coefficient estimates and Hankel determinants, which reveal important geometric information. This paper introduces a comprehensive subclass of analytic-univalent functions that generalizes well-known families like Yamaguchi and starlike functions within the broader Bazilević framework. Methods and Results: Using the theory of Ma-Minda functions and the principle of subordination, sharp bounds for the initial coefficients, the Fekete-Szegö functionals with parameters, and the Hankel determinants are established for this subclass. The results are proven to be sharp, meaning they are the best possible. Furthermore, it is shown that this general class reduces to several previously known function families for specific parameter values, demonstrating its wide applicability. Conclusions: This research successfully defines and analyzes a comprehensive subclass of analytic and univalent functions. The obtained sharp bounds for coefficient-related problems generalize and extend existing results in the literature. The work provides a unified framework for studying various function families, contributing valuable insights and tools for further exploration in Geometric Function Theory.
Source: F1000Research
Authors: Nathir Khaled, Abdul Rahman S.Juma
Institution: University of Anbar
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $1,350
OpenAlex ID: W7128922829