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Covering and distortion theorems for planar harmonic univalent mappings |
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| Authors: | Shaolin Chen Saminathan Ponnusamy Xiantao Wang |
| Affiliation: | 1. Department of Mathematics and Computational Science, Hengyang Normal University, Hengyang, Hunan, 421008, People’s Republic of China 2. Indian Statistical Institute (ISI), Chennai Centre, SETS (Society for Electronic Transactions and security), MGR Knowledge City, CIT Campus, Taramani, Chennai, 600113, India 3. Department of Mathematics, Hunan Normal University, Changsha, Hunan, 410081, People’s Republic of China |
| Abstract: | In this paper, we investigate Clunie and Sheil-Small’s covering theorems for sense-preserving planar harmonic univalent mappings defined in the unit disk. Our results significantly improve the earlier known result. Also, we obtain a distortion theorem for fully starlike harmonic mappings in the unit disk. |
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