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

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.