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.


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


Starlike; Convex
Full Text: DOI


[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
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.