Some Properties and Regions of Variability of Affine Harmonic Mappings and Affine Biharmonic Mappings
We first obtain the relations of local univalency, convexity, and linear connectedness between analytic functions and their corresponding affine harmonic mappings. In addition, the paper deals with the regions of variability of values of affine harmonic and biharmonic mappings. The regions (their bo...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Wiley
2009-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2009/834215 |
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| _version_ | 1832562545071751168 |
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| author | Sh. Chen S. Ponnusamy X. Wang |
| author_facet | Sh. Chen S. Ponnusamy X. Wang |
| author_sort | Sh. Chen |
| collection | DOAJ |
| description | We first obtain the relations of local univalency, convexity, and linear connectedness between analytic functions and their corresponding affine harmonic mappings. In addition, the paper deals with the regions of variability of values of affine harmonic and biharmonic mappings. The regions (their boundaries) are determined explicitly and the proofs rely on Schwarz lemma or subordination. |
| format | Article |
| id | doaj-art-94a4109c85d640bd8e4fdd9fc77f0f6d |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2009-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-94a4109c85d640bd8e4fdd9fc77f0f6d2025-02-03T01:22:21ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252009-01-01200910.1155/2009/834215834215Some Properties and Regions of Variability of Affine Harmonic Mappings and Affine Biharmonic MappingsSh. Chen0S. Ponnusamy1X. Wang2Department of Mathematics, Hunan Normal University, Changsha, Hunan 410081, ChinaDepartment of Mathematics, Indian Institute of Technology Madras, Chennai 600 036, IndiaDepartment of Mathematics, Hunan Normal University, Changsha, Hunan 410081, ChinaWe first obtain the relations of local univalency, convexity, and linear connectedness between analytic functions and their corresponding affine harmonic mappings. In addition, the paper deals with the regions of variability of values of affine harmonic and biharmonic mappings. The regions (their boundaries) are determined explicitly and the proofs rely on Schwarz lemma or subordination.http://dx.doi.org/10.1155/2009/834215 |
| spellingShingle | Sh. Chen S. Ponnusamy X. Wang Some Properties and Regions of Variability of Affine Harmonic Mappings and Affine Biharmonic Mappings International Journal of Mathematics and Mathematical Sciences |
| title | Some Properties and Regions of Variability of Affine Harmonic Mappings and Affine Biharmonic Mappings |
| title_full | Some Properties and Regions of Variability of Affine Harmonic Mappings and Affine Biharmonic Mappings |
| title_fullStr | Some Properties and Regions of Variability of Affine Harmonic Mappings and Affine Biharmonic Mappings |
| title_full_unstemmed | Some Properties and Regions of Variability of Affine Harmonic Mappings and Affine Biharmonic Mappings |
| title_short | Some Properties and Regions of Variability of Affine Harmonic Mappings and Affine Biharmonic Mappings |
| title_sort | some properties and regions of variability of affine harmonic mappings and affine biharmonic mappings |
| url | http://dx.doi.org/10.1155/2009/834215 |
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