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On strongly starlike multivalent functions of order \(\beta \) and type \(\alpha \). (English) Zbl 1195.30032

Summary: For analytic \(p\)-valent functions \(f (z)\) in the open unit disk \(\mathbb U\), a new subclass \(\tilde \mathcal S^*_p(\alpha , \beta )\) 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 \(\tilde \mathcal S^*_p(\alpha , \beta )\). In particular, our results extend and improve some results given by M. Nunokawa, S. Owa, H. Saitoh, A. Ikeda and N. Koike [J. Math. Anal. Appl. 212, No.1, 98–106 (1997; Zbl 0880.30012)].

MSC:

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

Citations:

Zbl 0880.30012
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References:

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