Sufficient conditions for starlikeness of order αα for meromorphic functions

Let ΣΣ be the class of functions F(z)F(z) which are meromorphic in the punctured open unit disk U∗U∗. Applying the results by Nunokawa [M. Nunokawa, On properties of non-Carathéodory functions, Proc. Japan Acad. 68 (1992) 152–153] and Fukui and Sakaguchi [S. Fukui and K. Sakaguchi, An extension of a theorem of S. Ruscheweyh, Bull. Fac. Edu. Wakayama Univ. Nat. Sci. 29 (1980) 1–3], we derive some sufficient conditions for meromorphic strongly starlikeness for function F(z)∈ΣF(z)∈Σ with some interesting corollaries.