The Properties of a New Subclass of Harmonic Univalent Mappings
We introduced a new subclass of univalent harmonic functions defined by the shear construction in the present paper. First, we showed that the convolutions of two special subclass harmonic mappings are convex in the horizontal direction. Secondly, we proved a necessary and sufficient condition for t...
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2013/794108 |
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| _version_ | 1832550721011056640 |
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| author | Zhi-Hong Liu Ying-Chun Li |
| author_facet | Zhi-Hong Liu Ying-Chun Li |
| author_sort | Zhi-Hong Liu |
| collection | DOAJ |
| description | We introduced a new subclass of univalent harmonic functions defined by the shear construction in the present paper. First, we showed that the convolutions of two special subclass harmonic mappings are convex in the horizontal direction. Secondly, we proved a necessary and sufficient condition for the above subclass of harmonic mappings to be convex in the horizontal direction. We also presented some basic examples of univalent harmonic functions explaining the behavior of the image domains. |
| format | Article |
| id | doaj-art-b7de3edc97d242a88cbe0e8ed81f2f46 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-b7de3edc97d242a88cbe0e8ed81f2f462025-02-03T06:06:02ZengWileyAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/794108794108The Properties of a New Subclass of Harmonic Univalent MappingsZhi-Hong Liu0Ying-Chun Li1College of Mathematics, Honghe University, Mengzi, Yunnan 661199, ChinaCollege of Mathematics, Honghe University, Mengzi, Yunnan 661199, ChinaWe introduced a new subclass of univalent harmonic functions defined by the shear construction in the present paper. First, we showed that the convolutions of two special subclass harmonic mappings are convex in the horizontal direction. Secondly, we proved a necessary and sufficient condition for the above subclass of harmonic mappings to be convex in the horizontal direction. We also presented some basic examples of univalent harmonic functions explaining the behavior of the image domains.http://dx.doi.org/10.1155/2013/794108 |
| spellingShingle | Zhi-Hong Liu Ying-Chun Li The Properties of a New Subclass of Harmonic Univalent Mappings Abstract and Applied Analysis |
| title | The Properties of a New Subclass of Harmonic Univalent Mappings |
| title_full | The Properties of a New Subclass of Harmonic Univalent Mappings |
| title_fullStr | The Properties of a New Subclass of Harmonic Univalent Mappings |
| title_full_unstemmed | The Properties of a New Subclass of Harmonic Univalent Mappings |
| title_short | The Properties of a New Subclass of Harmonic Univalent Mappings |
| title_sort | properties of a new subclass of harmonic univalent mappings |
| url | http://dx.doi.org/10.1155/2013/794108 |
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