International Journal of Mathematics and Mathematical Sciences 
Volume 14 (1991), Issue 3, Pages 619-623
doi:10.1155/S0161171291000856

Some sufficient conditions for univalence

Sukhjit Singh

Department of Mathematics, Punjabi University, Patiala 147002, (Punjab), India

Received 5 May 1989; Revised 1 January 1990

Abstract

A new subclass R(α), 0α1, of the class St(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.