Research Article

Geometric characterizations of some analytic functions related to the generalized Marcum Q-function

Published in: Quaestiones Mathematicae
Volume 48 , issue 12 , 2025 , pages: 1823–1844

DOI: 10.2989/16073606.2025.2549939

Author(s): Abdulaziz Alenazi College of Science, Northern Border University, Saudi Arabia , Khaled Mehrez Kairouan Preparatory Institute for Engineering Studies, University of Kairouan, Tunisia

Keywords: Primary: 30C45 , Secondary: 33C15 , The generalized Marcum Q-function , univalent functions , analytic functions , convex function

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Abstract

The aim of this paper is to study certain geometric properties, such as convexity of order α (0 ≤ α < 1) and uniform convexity inside the unit disk, for a class of analytic functions related to the generalized Marcum Q-function. Additionally, we investigate similar results for a class of functions associated with the lower incomplete generalized hypergeometric function. Moreover, we found sufficient conditions on the parameters of a certain class of analytic functions associated with the generalized Marcum Q-function, which allow us to conclude that they belong to some subclasses of the class of univalent functions.

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