Subordination properties of certain classes of multivalently analytic functions. (English) Zbl 1201.30019

Summary: By using a method based upon the principle of the Briot-Bouquet differential subordination, we obtain a sharp result for \(p\)-valently starlikeness of certain normalized and multivalently analytic functions. Our investigation of such families of multivalently analytic functions is motivated essentially by a recent study by M. Nunokawa, S. Owa, T. Sekine, R. Yamakawa, H. Saitoh and J. Nishiwaki [Int. J. Math. Math. Sci. 2007, Article ID 72393, 5 p. (2007; Zbl 1139.30305)]. We also give an answer to the open problem which was posed in the aforementioned article by Nunokawa et al.


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


Zbl 1139.30305
Full Text: DOI


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