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A certain connection between starlike and convex functions. (English) Zbl 1064.30008

Summary: We define two certain classes of functions \(S^{\ast}(\alpha,\beta)\) and \(C(\alpha,\beta)\) and obtain a certain connection between these classes.

MSC:

30C45 Special classes of univalent and multivalent functions of one complex variable (starlike, convex, bounded rotation, etc.)

Keywords:

Starlike; Convex
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References:

[1] M. Nunokawa, S. Owa, H. Saitoh, N.E. Cho and N. Takahashi, Some properties of analytic functions at extremal points for arguments, (submitted).
[2] Nunokawa, M., On the order of strongly starlikeness of strongly convex functions, (), 234-237, (7) · Zbl 0793.30007
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