In the present paper, we obtain several sufficient conditions for Carath?odory functions in the open unit disk U = {z ? C : ?z? < 1}. We also obtain sufficient conditions for p-valent or starlike functions. Moreover, we improve some results due to Nunokawa [Tsukuba J. Math. 13 (1989), 453-455] as some special cases of main results.
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Nunokawa et al. (2018) studied this question.
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