  In this paper, we determine the radius of uniform convexity for three kinds
of normalized Bessel functions of the first kind. In the mentioned cases the
normalized Bessel functions are uniformly convex on the determined disks.
Moreover, necessary and sufficient conditions are given for the parameters of
the three normalized functions such that they to be uniformly convex in the
open unit disk. The basic tool of this study is the development of Bessel
functions in function series.
