On an Integral Transform of a Class of Analytic Functions

Abstract

For and , let denote the class of all normalized analytic functions in the open unit disc such that , for some . It is known (Noshiro (1934) and Warschawski (1935)) that functions in are close-to-convex and hence univalent for . For , we consider the integral transform , where is a nonnegative real-valued integrable function satisfying the condition . The aim of present paper is, for given , to find sharp values of such that (i) whenever and (ii) whenever .