Note on the Coefficient Conjecture of Clunie and Sheil-Small on the univalent harmonic mapping
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866910022176342016 |
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| author | Mishra, Omendra Çetinkaya, Asena |
| author_facet | Mishra, Omendra Çetinkaya, Asena |
| contents | In this article, we construct generalized harmonic univalent mappings and find its coefficients bounds. We present the counterexample to validate the coefficient conjecture proposed by Clunie and Sheil-Small for the class of functions $f=h+\overline{g}\in \mathcal{S}_{\mathcal{H}}$ with the help of these examples we improve the conjecture bounds of class $\mathcal{S}_{\mathcal{H}}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_13613 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Note on the Coefficient Conjecture of Clunie and Sheil-Small on the univalent harmonic mapping Mishra, Omendra Çetinkaya, Asena Complex Variables 31A05, 30C45, 30C55 In this article, we construct generalized harmonic univalent mappings and find its coefficients bounds. We present the counterexample to validate the coefficient conjecture proposed by Clunie and Sheil-Small for the class of functions $f=h+\overline{g}\in \mathcal{S}_{\mathcal{H}}$ with the help of these examples we improve the conjecture bounds of class $\mathcal{S}_{\mathcal{H}}$. |
| title | Note on the Coefficient Conjecture of Clunie and Sheil-Small on the univalent harmonic mapping |
| topic | Complex Variables 31A05, 30C45, 30C55 |
| url | https://arxiv.org/abs/2602.13613 |