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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.

MSC:

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

[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
[2] Jack, I.S., Functions starlike and convex of order \(\alpha\), J. London math. soc., 3, 469-474, (1971) · Zbl 0224.30026
[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-Carath√©odory functions, Proc. Japan acad., 68, 152-153, (1992) · Zbl 0773.30020
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