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arXiv · 1303.1263

A sufficient condition for $p$-valently harmonic functions

Toshio Hayami
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Abstract

For normalized harmonic functions $f(z)=h(z)+\bar{g(z)}$ in the open unit disk $\mathbb{U}$, a sufficient condition on $h(z)$ for $f(z)$ to be $p$-valent in $\mathbb{U}$ is discussed. Moreover, some interesting examples and images of $f(z)$ satisfying the obtained condition are enumerated.

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Toshio Hayami. 2013-03-06. A sufficient condition for $p$-valently harmonic functions. https://doi.org/10.1080/17476933.2013.826656

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