Journal of Inequalities and Applications
Volume 2010 (2010), Article ID 896087, 6 pages
Research Article

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

Department of Mathematics and Computer Science, İstanbul Kültür University, İstanbul 31456, Turkey

Received 3 June 2010; Accepted 26 July 2010

Academic Editor: N. Govil

Copyright © 2010 Yaşar Polatoğlu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Any harmonic function in the open unit disc 𝔻={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.