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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| Sujets: | |
| Accès en ligne: | https://arxiv.org/abs/2511.05076 |
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| _version_ | 1866911253579956224 |
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| author | Biswas, Raju Mandal, Rajib |
| author_facet | Biswas, Raju Mandal, Rajib |
| contents | In this paper, we introduce definitions of the pre-Schwarzian and the Schwarzian derivatives for any locally univalent log-harmonic mappings defined in the unit disk $\mathbb{D}=\{z\in\mathbb{C}: |z|<1\}$. We explore the properties and applications of these concepts in the context of geometric function theory, and we also establish a necessary and sufficient condition for a non-vanishing log-harmonic mapping having a finite pre-Schwarzian norm. Additionally, we establish a relationship between the pre-Schwarzian norm of a non-vanishing log-harmonic mapping and that of a certain analytic function in $\mathbb{D}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_05076 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the pre-Schwarzian and Schwarzian derivatives of log-harmonic mappings Biswas, Raju Mandal, Rajib Complex Variables 31A05, 30C35, 30C45, 30C62 In this paper, we introduce definitions of the pre-Schwarzian and the Schwarzian derivatives for any locally univalent log-harmonic mappings defined in the unit disk $\mathbb{D}=\{z\in\mathbb{C}: |z|<1\}$. We explore the properties and applications of these concepts in the context of geometric function theory, and we also establish a necessary and sufficient condition for a non-vanishing log-harmonic mapping having a finite pre-Schwarzian norm. Additionally, we establish a relationship between the pre-Schwarzian norm of a non-vanishing log-harmonic mapping and that of a certain analytic function in $\mathbb{D}$. |
| title | On the pre-Schwarzian and Schwarzian derivatives of log-harmonic mappings |
| topic | Complex Variables 31A05, 30C35, 30C45, 30C62 |
| url | https://arxiv.org/abs/2511.05076 |