Harmonic mappings related to Janowski starlike functions

Abstract

Let S * be the class of starlike functions and let SH be the class of harmonic mappings in the plane. In this paper we investigate harmonic mapping related to the starlike functions.

Some classes of harmonic mappings with analytic part defined by subordination

“…We provide coefficient estimates, distortion, and area estimates, and covering theorems of the classes. The results presented here generalize the main results in [9,13,14,32]. Now we introduce the following classes.…”

“…Kahramaner et al [13] investigated the class of harmonic mappings related to Janowski starlike functions. Zhu and Huang [32] studied the distortion theorems for harmonic mappings with analytic parts of convex or starlike functions of order β .…”

“…Also, Hotta and Michalski [9] studied the properties of a subclass of L H having starlike analytic part h and obtained coefficient, distortion, and growth estimates of g , and Jacobian estimates of f . Kahramaner et al [13] investigated the class of harmonic mappings related to Janowski starlike functions. Zhu and Huang [32] studied the distortion theorems for harmonic mappings with analytic parts of convex or starlike functions of order β .…”