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Zbl 1195.30032
Xu, N-eng; Yang, Ding-Gong; Owa, Shigeyoshi
On strongly starlike multivalent functions of order $\beta$ and type $\alpha$.
(English)
[J] Math. Nachr. 283, No. 8, 1207-1218 (2010). ISSN 0025-584X; ISSN 1522-2616/e

Summary: For analytic $p$-valent functions $f (z)$ in the open unit disk $\Bbb U$, a new subclass $\tilde \cal S^*_p(\alpha , \beta )$ consisting of the functions $f (z)$ which are strongly starlike $p$-valent of order $\beta$ and type $\alpha$ is introduced. The object of the present paper is to derive some sufficient conditions for $f (z)$ to be in the class $\tilde \cal S^*_p(\alpha , \beta )$. In particular, our results extend and improve some results given by {\it M. Nunokawa, S. Owa, H. Saitoh, A. Ikeda} and {\it N. Koike} [J. Math. Anal. Appl. 212, No.1, 98--106 (1997; Zbl 0880.30012)].
MSC 2000:
*30C45 Special classes of univalent and multivalent functions

Keywords: multivalent function; starlike function; subordination

Citations: Zbl 0880.30012

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