Sufficient Conditions for Caratheodory Functions

Mamoru Nunokawa, Oh Sang Kwon, Young Jae Sim, Nak Eun Cho


In the present paper, we obtain several sufficient conditions for Carath\'eodory functions in the open unit disk $\mathbb{U}=\1\{ z\in\mathbb{C}:|z|<1 \2\}$. We also obtain sufficient conditions for $p$-valent or starlike functions. Moreover, we improve some results due to Nunokawa [Tsukuba J. Math., {\bf 13}(2) (1989), 453--455] as some special cases of main results.

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