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On certain subclasses of bounded univalent functions

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Fuka J., Jakubowski Z.

Annales Polonici Mathematici

1991

tom 55

nr 1

109-115

Let 𝔻 = {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 𝔻, and by S(M), M > 1, the subclass of functions f of the family S such that |f(z)| < M in 𝔻. 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 $arc I_α = I_α(f) ⊂ T$ of length 2πα such that $\overline{lim}_{z→ z₀, z ∈ 𝔻 } |f(z)| ≤ M$ for every $z₀ ∈ I_α$ and $\overline{lim}_{z→ z₀,z∈ 𝔻 } |f(z)|≤ m$ for every $z₀ ∈ T \ Ī_α$.

Ograniczanie wyników

1 Annales Polonici Mathematici

1 Fuka J.

1 Jakubowski Z.

1 1991

Wyniki wyszukiwania

On certain subclasses of bounded univalent functions