Application of the Subordination Principle to the Harmonic Mappings Convex in One Direction with Shear Construction Method

Any harmonic function in the open unit disc can be written as a sum of an analytic and antianalytic functions , where and are analytic functions in and are called the analytic part and the coanalytic part of 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.