Radii of the $\beta -$uniformly convex of order $\alpha$ of Lommel and Struve functions

TL;DR

This paper determines the radii within which certain normalized Lommel and Struve functions are $eta$-uniformly convex of a given order, expanding understanding of their geometric properties.

Contribution

It establishes the radii of $eta$-uniform convexity of order $oldsymbol{\alpha}$ for three types of normalized Lommel and Struve functions of the first kind.

Findings

Normalized functions are $eta$-uniformly convex within specific disks.

The study uses series representations of Lommel and Struve functions.

Results provide explicit radii for $eta$-uniform convexity of these functions.

Abstract

In this paper, we determine the radii of $\beta -$uniformly convex of order $\alpha $ for three kinds of normalized Lommel and Struve functions of the first kind. In the cases considered the normalized Lommel and Struve functions are $\beta -$uniformly convex functions of order $\alpha $ on the determined disks. The basic tool of this study is Lommel and Struve functions in series.