Subordination properties of certain classes of multivalently analytic functions

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 Nunokawa et al. [M. Nunokawa, S. Owa, T. Sekine, R. Yamakawa, H. Saitoh and J. Nishiwaki, On certain multivalent functions, Internat. J. Math. Math. Sci. 2007 (2007) 1–5. Article ID 72393]. We also give an answer to the open problem which was posed in the aforementioned article by Nunokawa et al.