Differential inequalities and Bessel functions

Abstract: Let denote the class of analytic functions defined on the unit disk with the normalization , in and satisfy the condition for all and for some real constants and such that . We find conditions on constants and such that functions in are univalent in . As a consequence of our investigation, we present univalence and starlikeness criteria. As applications, we present conditions such that is in , where denotes the suitably normalized form of the generalized Bessel functions of the first kind. [Copyright &y& Elsevier]