Sufficient conditions for starlikeness of order \(\alpha\) for meromorphic functions. (English) Zbl 1255.30023

Summary: Let \(\Sigma \) be the class of functions \(F(z)\) which are meromorphic in the punctured open unit disk. Applying the results by M. Nunokawa [Proc. Japan Acad., Ser. A 68, No. 6, 152–153 (1992; Zbl 0773.30020)] and S. Fukui and K. Sakaguchi [Bull. Fac. Edu. Wakayama Univ. Nat. Sci. 29, 1–3 (1980; Zbl 1255.30012)], we derive some sufficient conditions for meromorphic strong starlikeness for function \(F(z)\in \Sigma \) with some interesting corollaries.


30C45 Special classes of univalent and multivalent functions of one complex variable (starlike, convex, bounded rotation, etc.)
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[1] Fukui, S.; Sakaguchi, K., An extension of a theorem of S. Ruscheweyh, Bull. Fac. Edu. Wakayama Univ. Nat. Sci., 29, 1-3 (1980) · Zbl 1255.30012
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[3] Miller, S. S.; Mocanu, P. T., Second order differential inequalities in the complex plane, J. Math. Anal. Appl., 65, 289-305 (1978) · Zbl 0367.34005
[4] Nunokawa, M., On properties of non-Carathéodory functions, Proc. Japan Acad., 68, 152-153 (1992) · Zbl 0773.30020
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