Pre-Schwarzian norm estimation for functions in the Ma-Minda-type starlike and convex classes
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866912360423227392 |
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| author | Biswas, Raju |
| author_facet | Biswas, Raju |
| contents | In this paper, we establish the sharp estimates of the pre-Schwarzian norm of functions $f$ in the Ma-Minda type starlike and convex classes $\mathcal{S}^*(φ)$ and $\mathcal{C}(φ)$, respectively, whenever $φ(z)=3/\left(3+(α-3)z-αz^2\right)$ with $-3<α\leq 1$, $φ(z)=(1+z)(1-s z)$ with $-1/3\leq s\leq 1/3$ and $φ(z)=1+z/\left((1-z) (1+αz)\right)$ with $0\leq α\leq 1/2$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_01910 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Pre-Schwarzian norm estimation for functions in the Ma-Minda-type starlike and convex classes Biswas, Raju Complex Variables 30C45, 30C55, 30C80 In this paper, we establish the sharp estimates of the pre-Schwarzian norm of functions $f$ in the Ma-Minda type starlike and convex classes $\mathcal{S}^*(φ)$ and $\mathcal{C}(φ)$, respectively, whenever $φ(z)=3/\left(3+(α-3)z-αz^2\right)$ with $-3<α\leq 1$, $φ(z)=(1+z)(1-s z)$ with $-1/3\leq s\leq 1/3$ and $φ(z)=1+z/\left((1-z) (1+αz)\right)$ with $0\leq α\leq 1/2$. |
| title | Pre-Schwarzian norm estimation for functions in the Ma-Minda-type starlike and convex classes |
| topic | Complex Variables 30C45, 30C55, 30C80 |
| url | https://arxiv.org/abs/2505.01910 |