Radii problems for normalized hyper-Bessel function

TL;DR

This paper investigates the radii of starlikeness and convexity for normalized hyper-Bessel functions related to specific lemniscate and Janowski functions, enhancing understanding of their geometric properties.

Contribution

It determines the radii of starlikeness and convexity for normalized hyper-Bessel functions associated with lemniscate and Janowski functions, which is a novel geometric analysis.

Findings

Radii of starlikeness are established.

Radii of convexity are determined.

Results apply to functions with parameters within specified bounds.

Abstract

The main purpose of the present paper is to ascertain the radii of starlikeness and convexity associated with lemniscate of Bernoulli and the Janowski function, $(1+Az)/(1+Bz)$ for $-1\leq B<A\leq 1,$ of normalized hyper-Bessel function.