Abstract
Let $\mathcal{A}(p)$ be the class of functions $f(z)$, analytic in $|z| \lt 1$ in the complex plane, of the form $f(z) = z^p + \cdots$. We study the question, that naturally rises, about the relation between the expressions $\frac{zf^{(p)}(z)}{f^{(p-1)}(z)}$ and $\frac{zf^{(p-1)}(z)}{f^{(p-2)}(z)}$, when $f(z) \in \mathcal{A}(p)$. Some relations of this type imply that $f(z)$ is $p$-valent or $p$-valent starlike in $|z| \lt 1$.
Citation
Mamoru Nunokawa. Janusz Sokół. "On multivalent functions in the unit disc." Tsukuba J. Math. 41 (2) 251 - 263, December 2017. https://doi.org/10.21099/tkbjm/1521597625
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