On distortion of a class of analytic functions under a familly of operators

Abstract

Consider a family of integral operators and a related family of differential operators, both defined on a class of analytic functions holomorphic in the unit disk, distortion properties of the real part are derived from a general aspect. 1. Integral and differential operators. Let F denote the class of analytic functions which are holomorphic in the unit disk E = {| z |< 1}. Let F nad G be its subclasses consisting of f ∈ F normalized by f(0) = f ′(0) − 1 = 0 and f(0) = 1, respectively. In previous papers [3, 6] we have observed an integral operator L(a) defined on F , which is represented by L(a)f(z) = a ∫