An estimation of the pre-Schwarzian norm for certain classes of analytic functions
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866910121462857728 |
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| author | Allu, Vasudevarao Biswas, Raju Mandal, Rajib |
| author_facet | Allu, Vasudevarao Biswas, Raju Mandal, Rajib |
| contents | The primary objective of this paper is to establish the sharp estimates of the pre-Schwarzian norm for functions $f$ in the class $\mathcal{S}^*(φ)$ and $\mathcal{C}(φ)$ when $φ(z)=1/(1-z)^s$ with $0<s\leq 1$ and $φ(z)=(1+sz)^2$ with $0<s\leq 1/\sqrt{2}$, where $\mathcal{S}^*(φ)$ and $\mathcal{C}(φ)$ are the Ma-Minda type starlike and Ma-Minda type convex classes associated with $φ$, respectively. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_19132 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | An estimation of the pre-Schwarzian norm for certain classes of analytic functions Allu, Vasudevarao Biswas, Raju Mandal, Rajib Complex Variables 30C45, 30C55 The primary objective of this paper is to establish the sharp estimates of the pre-Schwarzian norm for functions $f$ in the class $\mathcal{S}^*(φ)$ and $\mathcal{C}(φ)$ when $φ(z)=1/(1-z)^s$ with $0<s\leq 1$ and $φ(z)=(1+sz)^2$ with $0<s\leq 1/\sqrt{2}$, where $\mathcal{S}^*(φ)$ and $\mathcal{C}(φ)$ are the Ma-Minda type starlike and Ma-Minda type convex classes associated with $φ$, respectively. |
| title | An estimation of the pre-Schwarzian norm for certain classes of analytic functions |
| topic | Complex Variables 30C45, 30C55 |
| url | https://arxiv.org/abs/2504.19132 |