Radii of $$\varvec{\alpha }$$ α -Convexity of Some Normalized Bessel Functions of the First Kind

Abstract

In this paper our aim is to determine the radii of \(\alpha -\)convexity of the normalized Bessel functions for two different kinds of normalization in the case when the order is between \(-2\) and \(-1\). The key tools in the proof of our main results are the Mittag-Leffler expansion for Bessel functions, properties of zeros of the Bessel functions and their derivatives and some inequalities for complex and real numbers.