Radius of Uniform Convexity of some special functions

TL;DR

This paper determines the radius of uniform convexity for specific normalized q-Bessel and Wright functions by solving functional equations, providing insights into their geometric properties.

Contribution

It introduces six normalized forms of q-Bessel functions and three normalizations of Wright functions, establishing their uniform convexity radii through functional equations.

Findings

Identified the smallest positive roots of functional equations as the radii

Derived explicit radii for six q-Bessel function forms

Established radii for three Wright function normalizations

Abstract

In this investigation our main aim is to determine the radius of uniform convexity of the some normalized q-Bessel and Wright functions. Here we consider six different normalized forms of q-Bessel functions, while we apply three different kinds of normalizations of Wright function. Also, we have shown that the obtained radii are the smallest positive roots of some functional equations.