Pre-Schwarzian and Schwarzian norm Estimates for class of Ozaki Close-to-Convex functions
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866917878756802560 |
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| author | Ahamed, Molla Basir Hossain, Rajesh |
| author_facet | Ahamed, Molla Basir Hossain, Rajesh |
| contents | The primary objective of this paper is to derive sharp bounds for the norms of the Schwarzian and pre-Schwarzian derivatives in the Ozaki close-to-convex functions $f$, expressed in terms of their value $f^{\prime\prime}(0)$, in particular, when the quantity is equal to zero. Additionally, we obtain sharp bounds for distortion and growth theorems. We will also derive the sharp bound of pre-Schwarzian norm for a certain class of harmonic mappings whose analytic part is fixed. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_18284 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Pre-Schwarzian and Schwarzian norm Estimates for class of Ozaki Close-to-Convex functions Ahamed, Molla Basir Hossain, Rajesh Complex Variables Primary 30C45, 30C55, Secondary 30C80, 31A10 The primary objective of this paper is to derive sharp bounds for the norms of the Schwarzian and pre-Schwarzian derivatives in the Ozaki close-to-convex functions $f$, expressed in terms of their value $f^{\prime\prime}(0)$, in particular, when the quantity is equal to zero. Additionally, we obtain sharp bounds for distortion and growth theorems. We will also derive the sharp bound of pre-Schwarzian norm for a certain class of harmonic mappings whose analytic part is fixed. |
| title | Pre-Schwarzian and Schwarzian norm Estimates for class of Ozaki Close-to-Convex functions |
| topic | Complex Variables Primary 30C45, 30C55, Secondary 30C80, 31A10 |
| url | https://arxiv.org/abs/2412.18284 |