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arXiv · 2605.18590

On starlikeness of $p$-valent analytic functions

Mamoru Nunokawa$·Janusz Sokol
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Abstract

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 $\alpha$.

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Mamoru Nunokawa$, Janusz Sokol. 2026-05-18. On starlikeness of $p$-valent analytic functions. https://arxiv.org/abs/2605.18590

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