Application Of The Subordination Principle To The Harmonic Mappings Convex In One Direction With Shear Construction Method

Abstract

Any harmonic function in the open unit disc D = {z vertical bar vertical bar z vertical bar < 1} can be written as a sum of an analytic and antianalytic functions f = h(z) + <(g(z))over bar>, where h(z) and g(z) are analytic functions in D and are called the analytic part and the coanalytic part of f, respectively. Many important questions in the study of the classes of functions are related to bounds on the modulus of functions (growth) or the modulus of the derivative (distortion). In this paper, we consider both of these questions.