An Innovative Result on the Radius of Convexity and Uniform Convexity of Normalised Bessel Function

This paper investigates the geometric properties of normalised Bessel functions of the first kind, focusing on the radii of convexity and uniform convexity. Using analytic techniques such as logarithmic differentiation and properties of zeros of the Bessel function. Additionally, we provide new proofs related to the order convexity and compare our results with existing results to reveal interesting relationships, and we provide a graphical interpretation that supports the analytical findings.