The Landau-type theorems for functions with logharmonic Laplacian and bounded length distortions
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866913688070389760 |
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| author | Guin, Sudip Kumar Mandal, Rajib |
| author_facet | Guin, Sudip Kumar Mandal, Rajib |
| contents | In this study, we establish certain Landau-type theorems for functions with logharmonic Laplacian of the form $F(z)=|z|^2L(z)+K(z)$, $|z|<1$, where $L$ is logharmonic and $K$ is harmonic, with $L$ and $K$ having bounded length distortion in the unit disk $\mathbb{D}=\{z\in\mathbb{C}:|z|<1\}$. Furthermore, we examine the univalence of the mappings $D(F)$, where $D$ is a differential operator. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2502_08390 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The Landau-type theorems for functions with logharmonic Laplacian and bounded length distortions Guin, Sudip Kumar Mandal, Rajib Complex Variables In this study, we establish certain Landau-type theorems for functions with logharmonic Laplacian of the form $F(z)=|z|^2L(z)+K(z)$, $|z|<1$, where $L$ is logharmonic and $K$ is harmonic, with $L$ and $K$ having bounded length distortion in the unit disk $\mathbb{D}=\{z\in\mathbb{C}:|z|<1\}$. Furthermore, we examine the univalence of the mappings $D(F)$, where $D$ is a differential operator. |
| title | The Landau-type theorems for functions with logharmonic Laplacian and bounded length distortions |
| topic | Complex Variables |
| url | https://arxiv.org/abs/2502.08390 |