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.)

Zbl 0880.30012
Full Text:

References:

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