Landau-Type Theorems for Certain Biharmonic Mappings
Let F(z)=|z|2g(z)+h(z) (|z|<1) be a biharmonic mapping of the unit disk 𝔻, where g and h are harmonic in 𝔻. In this paper, the Landau-type theorems for biharmonic mappings of the form L(F) are provided. Here L represents the linear complex operator L=(z∂/∂z)-(z¯∂/∂z)¯ defined on the class of com...
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2014-01-01
|
| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/925947 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832556487004651520 |
|---|---|
| author | Ming-Sheng Liu Zhen-Xing Liu Jun-Feng Xu |
| author_facet | Ming-Sheng Liu Zhen-Xing Liu Jun-Feng Xu |
| author_sort | Ming-Sheng Liu |
| collection | DOAJ |
| description | Let F(z)=|z|2g(z)+h(z) (|z|<1) be a biharmonic mapping of the unit disk 𝔻, where g and h are harmonic in 𝔻. In this paper, the Landau-type theorems for biharmonic mappings of the form L(F) are provided. Here L represents the linear complex operator L=(z∂/∂z)-(z¯∂/∂z)¯ defined on the class of complex-valued C1 functions in the plane. The results, presented in this paper, improve the related results of earlier authors. |
| format | Article |
| id | doaj-art-9f76e77b7c9f4842b6172150db7c8b7d |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-9f76e77b7c9f4842b6172150db7c8b7d2025-02-03T05:45:13ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/925947925947Landau-Type Theorems for Certain Biharmonic MappingsMing-Sheng Liu0Zhen-Xing Liu1Jun-Feng Xu2School of Mathematical Sciences, South China Normal University, Guangzhou, Guangdong 510631, ChinaSchool of Mathematical Sciences, South China Normal University, Guangzhou, Guangdong 510631, ChinaDepartment of Mathematics, Wuyi University, Jiangmen, Guangdong 529020, ChinaLet F(z)=|z|2g(z)+h(z) (|z|<1) be a biharmonic mapping of the unit disk 𝔻, where g and h are harmonic in 𝔻. In this paper, the Landau-type theorems for biharmonic mappings of the form L(F) are provided. Here L represents the linear complex operator L=(z∂/∂z)-(z¯∂/∂z)¯ defined on the class of complex-valued C1 functions in the plane. The results, presented in this paper, improve the related results of earlier authors.http://dx.doi.org/10.1155/2014/925947 |
| spellingShingle | Ming-Sheng Liu Zhen-Xing Liu Jun-Feng Xu Landau-Type Theorems for Certain Biharmonic Mappings Abstract and Applied Analysis |
| title | Landau-Type Theorems for Certain Biharmonic Mappings |
| title_full | Landau-Type Theorems for Certain Biharmonic Mappings |
| title_fullStr | Landau-Type Theorems for Certain Biharmonic Mappings |
| title_full_unstemmed | Landau-Type Theorems for Certain Biharmonic Mappings |
| title_short | Landau-Type Theorems for Certain Biharmonic Mappings |
| title_sort | landau type theorems for certain biharmonic mappings |
| url | http://dx.doi.org/10.1155/2014/925947 |
| work_keys_str_mv | AT mingshengliu landautypetheoremsforcertainbiharmonicmappings AT zhenxingliu landautypetheoremsforcertainbiharmonicmappings AT junfengxu landautypetheoremsforcertainbiharmonicmappings |