On analytic functions related to Booth-lemniscate
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866911163377254400 |
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| author | Ali, Md Firoz Nurezzaman, Md Thakur, Lokenath |
| author_facet | Ali, Md Firoz Nurezzaman, Md Thakur, Lokenath |
| contents | For $0\le α\le 1 $, let $\mathcal{BS}(α)$ be the class of all analytic functions in the unit disk $\mathbb{D}:=\{~z\in\mathbb{C}:|z|<1\}$ with normalization $f(0)=0$ and $f'(0)=1$ that satisfy the subordinate relation $zf'(z)/f(z)-1\prec z/(1-αz^2)$ and $\mathcal{BK}(α)$ be the class of all functions $f$ for which $zf' \in \mathcal{BS}(α)$. In this article, we obtain a sharp estimate of the initial Taylor coefficients and logarithmic coefficients for functions in the classes $\mathcal{BS}(α)$ and $\mathcal{BK}(α)$. Further, we obtain the radius of convexity and study the pre-Schwarzian norm for the classes $\mathcal{BS}(α)$ and $\mathcal{BK}(α)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_15534 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On analytic functions related to Booth-lemniscate Ali, Md Firoz Nurezzaman, Md Thakur, Lokenath Complex Variables 30C45, 30C55 For $0\le α\le 1 $, let $\mathcal{BS}(α)$ be the class of all analytic functions in the unit disk $\mathbb{D}:=\{~z\in\mathbb{C}:|z|<1\}$ with normalization $f(0)=0$ and $f'(0)=1$ that satisfy the subordinate relation $zf'(z)/f(z)-1\prec z/(1-αz^2)$ and $\mathcal{BK}(α)$ be the class of all functions $f$ for which $zf' \in \mathcal{BS}(α)$. In this article, we obtain a sharp estimate of the initial Taylor coefficients and logarithmic coefficients for functions in the classes $\mathcal{BS}(α)$ and $\mathcal{BK}(α)$. Further, we obtain the radius of convexity and study the pre-Schwarzian norm for the classes $\mathcal{BS}(α)$ and $\mathcal{BK}(α)$. |
| title | On analytic functions related to Booth-lemniscate |
| topic | Complex Variables 30C45, 30C55 |
| url | https://arxiv.org/abs/2509.15534 |