On starlikeness of $p$-valent analytic functions
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866916023187275776 |
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| author | Nunokawa$, Mamoru Sokol, Janusz |
| author_facet | Nunokawa$, Mamoru Sokol, Janusz |
| contents | The known Ozaki's condition says that $\mathfrak{Re}\left\{f^{(p)}(z)\right\}>0$ for $|z|<1$ implies that $f(z)=z^p+a_{p+1}z^{p+1}+\cdots$ is at most $p$-valent in $\mathbb D$. In this paper prove an extension of Ozaki's condition. Also, we shall determine the new sufficient conditions for functions to be in the class of $p$-valent starlike of order $α$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2605_18590 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On starlikeness of $p$-valent analytic functions Nunokawa$, Mamoru Sokol, Janusz Complex Variables 30C45 The known Ozaki's condition says that $\mathfrak{Re}\left\{f^{(p)}(z)\right\}>0$ for $|z|<1$ implies that $f(z)=z^p+a_{p+1}z^{p+1}+\cdots$ is at most $p$-valent in $\mathbb D$. In this paper prove an extension of Ozaki's condition. Also, we shall determine the new sufficient conditions for functions to be in the class of $p$-valent starlike of order $α$. |
| title | On starlikeness of $p$-valent analytic functions |
| topic | Complex Variables 30C45 |
| url | https://arxiv.org/abs/2605.18590 |