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Some sufficient conditions for starlikeness and convexity. (English) Zbl 1195.30030
Summary: There are many results for sufficient conditions of functions \(f(z)\) which are analytic in the open unit disc \(\mathbb U\) to be starlike and convex in \(\mathbb U\). In view of the results due to S. Ozaki, I. Ono and T. Umezawa [Sci. Rep. Tokyo Kyoiku Daigaku, Sect. A 5, 111–114 (1956; Zbl 0071.29501)], P.T. Mocanu [Rev. Roum. Math. Pures Appl. 33, No.1–2, 116–124 (1988; Zbl 0652.30004)], and M. Nunokawa [Proc. Japan Acad., Ser. A 69, No.7, 234–237 (1993; Zbl 0793.30007)], some sufficient conditions for starlikeness and convexity of \(f(z)\) are discussed.

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