On certain subclasses of bounded univalent functions
J. Fuka ; Z. J. Jakubowski
Annales Polonici Mathematici, Tome 55 (1991), p. 109-115 / Harvested from The Polish Digital Mathematics Library
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Let = z ∈ ℂ; |z| < 1, T = z ∈ ℂ; |z|=1. Denote by S the class of functions f of the form f(z) = z + a₂z² + ... holomorphic and univalent in , and by S(M), M > 1, the subclass of functions f of the family S such that |f(z)| < M in . We introduce (and investigate the basic properties of) the class S(M,m;α), 0 < m ≤ M < ∞, 0 ≤ α ≤ 1, of bounded functions f of the family S for which there exists an open arcIα=Iα(f)⊂T of length 2πα such that lim¯z→z₀,z∈|f(z)|≤M for every z₀∈Iα and lim¯z→z₀,z∈|f(z)|≤m for every z₀∈TĪα.

Publié le : 1991-01-01
EUDML-ID : urn:eudml:doc:262312 
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     title = {On certain subclasses of bounded univalent functions},
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     year = {1991},
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J. Fuka; Z. J. Jakubowski. On certain subclasses of bounded univalent functions. Annales Polonici Mathematici, Tome 55 (1991) pp. 109-115. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-apmv55z1p109bwm/

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