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Extensions of sufficient conditions for starlikeness and convexity of order \(\alpha \). (English) Zbl 1216.30023
Summary: For analytic functions \(f(z)\) in the open unit disk \(\mathbb U\), there are many sufficient conditions for \(f(z)\) to be starlike and convex in \(\mathbb U\). In view of the paper by P. T. Mocanu [Rev. Roum. Math. Pures Appl. 33, No. 1–2, 116–124 (1988; Zbl 0652.30004)], some extensions of sufficient conditions for \(f(z)\) to be starlike of order \(\alpha \) and to be convex of order \(\alpha \) are discussed.

30C45 Special classes of univalent and multivalent functions of one complex variable (starlike, convex, bounded rotation, etc.)
Full Text: DOI
[1] Mocanu, P.T., Some starlikeness conditions for analytic functions, Rev. roumaine math. pures appl., 33, 117-124, (1988) · Zbl 0652.30004
[2] Mocanu, P.T., Some simple criteria for starlikeness and convexity, Libertas math., 13, 27-40, (1993) · Zbl 0793.30008
[3] Nunokawa, M.; Owa, S.; Polatoglu, Y.; Caglar, M.; Duman, E.Y., Some sufficient conditions for starlikeness and convexity, Turkish J. math., 34, 333-337, (2010) · Zbl 1195.30030
[4] Alexander, J.W., Functions which map the interior of the unit circle upon simple regions, Ann. of math., 17, 12-22, (1915) · JFM 45.0672.02
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