  Sufficient conditions are determined on the parameters such that the
generalized and normalized Bessel function of the first kind and other related
functions belong to subclasses of starlike and convex functions defined in the
unit disk associated with the exponential mapping. Several differential
subordination implications are derived for analytic functions involving Bessel
function and the operator introduced by Baricz \emph{et al.} [Differential
subordinations involving generalized Bessel functions, Bull. Malays. Math. Sci.
Soc. {\bf 38} (2015), no.~3, 1255--1280]. These results are obtained by
constructing suitable class of admissible functions. Examples involving
trigonometric and hyperbolic functions are provided to illustrate the obtained
results.
