Integral Operator of Analytic Functions with Positive Real Part

Abstract

In this paper, we introduce the integral operator (, , ; , , )(z) analytic functions with positive real part. The radius of convexity of this integral operator when = 1 is determined. In particular, we get the radius of starlikeness and convexity of the analytic functions with Re {f(z)/z} > 0 and Re {f'(z)} > 0. Furthermore, we derive sufficient condition for the integral operator (, , ; , , )(z) to be analytic and univalent in the open unit disc, which leads to univalency of the operators dt and .