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

Any harmonic function in the open unit discD {z | |z| < 1} can be written as a sum of an analytic and antianalytic functions f h z g z , 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.