Geometric Properties for a Class of Multivalent Convex Functions Using a Bessel-Based Integral Operator

Abstract: This This study pioneers the investigation into a novel class of multivalent convex functions of order η, defined within the unit disk and constructed via an integral operator originating from the generalized Bessel equation. We developed a systematic methodology to derive the initial coefficients, subsequently employing advanced complex analysis to establish a series of sharp and foundational results. Crucially, we determined the precise upper bounds (Coefficient Bounds(, which are essential for understanding the function's growth limitations and series expansion. Furthermore, we proved Growth and Distortion theorems to delineate the exact geometric behavior and variability of these functions, which is vital for mapping and applications in complex analysis. One of the most important aspects in this study regarding the defined class is extracting a complete description of the extreme points. Identifying these points is paramount, as it facilitates the representation of any function in the class as a convex combination of these fundamental elements, thereby fully describing the geometric hull and confirming the sharpness of the established inequalities. Keywords: Bessel function; Coefficient bounds; Distortion Theorem, Growth Theorem and Integral operator. Title: Geometric Properties for a Class of Multivalent Convex Functions Using a Bessel-Based Integral Operator Author: Saba N. Al-Khafaji International Journal of Mathematics and Physical Sciences Research ISSN 2348-5736 (Online) Vol. 13, Issue 2, October 2025 - March 2026 Page No: 65-73 Research Publish Journals Website: www.researchpublish.com Published Date: 23-February-2026 DOI: https://doi.org/10.5281/zenodo.18742952 Paper Download Link (Source) https://www.researchpublish.com/papers/geometric-properties-for-a-class-of-multivalent-convex-functions-using-a-bessel-based-integral-operator