Properties of Some Classes of Planar Harmonic and Planar Biharmonic Mappings
| 详细信息 | 推荐本文 | |
- 作者：S. H. Chen (1) shlchen1982@yahoo.com.cn
S. Ponnusamy (2) samy@iitm.ac.in
X. Wang (1) xtwang@hunnu.edu.cn - 关键词：Planar harmonic mapping – ; Biharmonic mapping – ; The Schwarz lemma – ; The Landau theorem – ; Bloch constant – ; Linear connectivity
- 刊名：Complex Analysis and Operator Theory
- 出版时间：September 2011
- 出版年：2011
- 期刊代码：133_1661-8262
- 类别：mat
- 卷：5
- 期：3
- 页码：901-916
- 数据来源：sp
摘要
The aim of this paper is to investigate some properties of planar harmonic and biharmonic mappings. First, we use the Schwarz lemma and the improved estimates for the coefficients of planar harmonic mappings to generalize earlier results related to Landau’s constants for harmonic and biharmonic mappings. Second, we obtain a new Landau’s Theorem for a certain class of biharmonic mappings. At the end, we derive a relationship between the images of the linear connectivity of the unit disk \mathbbD{\mathbb{D}} under the planar harmonic mappings f=h+[`(g)]{f=h+\overline{g}} and under their corresponding analytic counterparts F = h − g.