Convexity of integral operators involving generalized Bessel functions

Abstract

The main object of this paper is to give sufficient conditions for certain families of integral operators which are defined by means of the normalized form of the generalized Bessel functions to be convex of given order in the open unit disk. In particular cases, we find the corresponding simple conditions for integral operators involving the Bessel function, the modified Bessel function and the spherical Bessel function.