Random iterations, fixed points and invariant CRF-horospheres in complex Banach spaces

For holomorphic noncontractive maps on (not necessarily bounded) domains in complex Banach spaces, we establish the conditions guaranteeing locally uniform convergence of random iterations and study the existence of fixed points and boundary behaviour of iterations. In particular, we show that the p...

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Vydané v:	Journal of mathematical analysis and applications Ročník 295; číslo 2; s. 291 - 302
Hlavní autori:	Włodarczyk, Kazimierz, Klim, Dorota
Médium:	Journal Article
Jazyk:	English
Vydavateľské údaje:	San Diego, CA Elsevier Inc 15.07.2004 Elsevier
Predmet:	Complex Banach space Exact sciences and technology Fixed point Functional analysis Functions of a complex variable Holomorphic noncontractive map Invariant CRF-horosphere Julia's lemma Mathematical analysis Mathematics Random iteration Sciences and techniques of general use Several complex variables and analytic spaces Unbounded domain Wolff's theorem Complex Banach space Random iteration Invariant CRF-horosphere Unbounded domain Wolff's theorem Julia's lemma Holomorphic noncontractive map Fixed point Uniform convergence Invariant Random fixed point Fix point Complex domain Mathematical analysis Iteration Holomorphic mapping Banach space
ISSN:	0022-247X, 1096-0813
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Shrnutí:	For holomorphic noncontractive maps on (not necessarily bounded) domains in complex Banach spaces, we establish the conditions guaranteeing locally uniform convergence of random iterations and study the existence of fixed points and boundary behaviour of iterations. In particular, we show that the problem, concerning the existence of the horospheres determined by Carathéodory–Reiffen–Finsler pseudometrics defined on unbounded domains, has the solution and we prove new results of type of Julia's lemma and Wolff's theorem.
ISSN:	0022-247X 1096-0813
DOI:	10.1016/j.jmaa.2003.10.054