Some sufficient conditions for univalence

Abstract

A new subclass R ( α ), 0 ≤ α ≤ 1, of the class S t (1/2) the class of starlike functions of order 1/2 is introduced and it is shown that R ( α ) is closed with respect to the Hadamard product of analytic functions. Some sufficient conditions for the normalized regular functions to be univalent in the unit disk E are given.