Work

Geometric Properties and Applications in System Modeling for a Generalized q-Symmetric Operator

Year: 2025

Type: article

Abstract: This paper introduces a novel generalized q-symmetric differential operator for studying a certain subclass of univalent functions with negative coefficients. We establish several significant theoretical results for this class, including sharp coefficient bounds and characterization theorems based on the generalized Hadamard product. Two significant applications demonstrate the theoretical framework’s practical utility. First, in the context of geometric modeling, we demonstrate how the function class and operator can be utilized to create and control complex, non-overlapping transformations. Second, in digital signal processing, we show that these functions serve as stable digital filter prototypes and that our operator is an effective tool for fine-tuning the filter’s frequency response. These applications bridge the gap between abstract geometric function theory and practical system design by demonstrating the operator’s versatility as a tool for analysis and synthesis.

Source: Symmetry

DOI: 10.3390/sym17101593

Authors: Abdelrahman M. Yehia, Atef F. Hashem, A. S. Al-Moisheer, Mohamed A. Sohaly, Samar M. Madian, Mohammed M. Tharwat

Institutions: Beni-Suef University, Imam Mohammad ibn Saud Islamic University, Mansoura University, Higher Institute of Engineering

Language: English

Topic: Analytic and geometric function theory

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $2,896

Funder: Al-Imam Muhammad Ibn Saud Islamic University