Title of article :
Coefficient Estimates and Landau-Bloch s Constant for Planar Harmonic Mappings
Author/Authors :
Chen, Sh Department of Mathematics - Hunan Normal University, Changsha, P. R. of China , Ponnusamy, S Department of Mathematics - Indian Institute of Technology Madras, India , Wang, X Department of Mathematics - Hunan Normal University, Changsha, P. R. of China
Abstract :
The aim of this paper is to study the properties of planar harmonic mappings. The main results are as follows. First, by using the subordination of analytic functions, a sharp coefficient estimate is obtained and several applications are given. Then two results about Landau-Bloch s constant are proved: one for planar harmonic mappings and the other for L(f), where L represents the linear complex operator L = z ∂/∂z - (overline)z ∂/∂z defined on the class of complex-valued C^1 functions in the plane and f is an open harmonic mapping.
Keywords :
Harmonic mapping , coefficient estimate , Landau s constant , Bloch s constant , open harmonic mapping , Schwarz s lemma , univalent mapping , subordination
Journal title :
Bulletin of the Malaysian Mathematical Sciences Society
Journal title :
Bulletin of the Malaysian Mathematical Sciences Society
