On a certain class of starlike functions
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866908273134796800 |
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| author | Ali, Md Firoz Nurezzaman, Md |
| author_facet | Ali, Md Firoz Nurezzaman, Md |
| contents | Let $\mathcal{S}_u^*$ denote the class of all analytic functions $f$ in the unit disk $\mathbb{D}:=\{z\in\mathbb{C}:|z|<1\}$, normalized by $f(0)=f'(0)-1=0$ that satisfies the inequality $\left|zf'(z)/f(z)-1\right|<1$ in $\mathbb{D}$. In the present article, we obtain the sharp estimate of Hankel determinants whose entries are coefficients of $f\in\mathcal{S}_u^*$, logarithmic coefficients of $f\in\mathcal{S}_u^*$ and coefficients of inverse of $f\in\mathcal{S}_u^*$, respectively. We also obtain, the sharp estimate of the successive coefficients for functions in the class $\mathcal{S}_u^*$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_13902 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On a certain class of starlike functions Ali, Md Firoz Nurezzaman, Md Complex Variables Let $\mathcal{S}_u^*$ denote the class of all analytic functions $f$ in the unit disk $\mathbb{D}:=\{z\in\mathbb{C}:|z|<1\}$, normalized by $f(0)=f'(0)-1=0$ that satisfies the inequality $\left|zf'(z)/f(z)-1\right|<1$ in $\mathbb{D}$. In the present article, we obtain the sharp estimate of Hankel determinants whose entries are coefficients of $f\in\mathcal{S}_u^*$, logarithmic coefficients of $f\in\mathcal{S}_u^*$ and coefficients of inverse of $f\in\mathcal{S}_u^*$, respectively. We also obtain, the sharp estimate of the successive coefficients for functions in the class $\mathcal{S}_u^*$. |
| title | On a certain class of starlike functions |
| topic | Complex Variables |
| url | https://arxiv.org/abs/2503.13902 |