منابع مشابه
A Julia–Carathéodory theorem for hyperbolically monotone mappings in the Hilbert ball
We establish a Julia–Carathéodory theorem and a boundary Schwarz– Wolff lemma for hyperbolically monotone mappings in the open unit ball of a complex Hilbert space. Let B be the open unit ball of a complex Hilbert space H with inner product 〈·, ·〉 and norm ‖ · ‖, and let ρ : B ×B 7→ R be the hyperbolic metric on B ([8], p. 98), i.e., ρ(x, y) = tanh √ 1− σ(x, y), (1) where σ(x, y) = (1 − ‖x‖)(1 ...
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Let $f$ be a locally univalent function on the unit disk $U$. We consider the normalized extensions of $f$ to the Euclidean unit ball $B^nsubseteqmathbb{C}^n$ given by $$Phi_{n,gamma}(f)(z)=left(f(z_1),(f'(z_1))^gammahat{z}right),$$ where $gammain[0,1/2]$, $z=(z_1,hat{z})in B^n$ and $$Psi_{n,beta}(f)(z)=left(f(z_1),(frac{f(z_1)}{z_1})^betahat{z}right),$$ in which $betain[0,1]$, $f(z_1)neq 0$ a...
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ژورنال
عنوان ژورنال: Journal of Mathematical Analysis and Applications
سال: 1985
ISSN: 0022-247X
DOI: 10.1016/0022-247x(85)90187-8