journal article Jul 27, 2000

Random iterations of holomorphic maps in complex Banach spaces

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Abstract
Conditions guaranteeing the uniform convergence to constant maps of random iterations of holomorphic contractions on unbounded domains in complex Banach spaces are established.
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References
26
[1]
Baker, I. N. "On compositions of analytic self-mappings of a convex domain" Arch. Math. (Basel) (1990) 10.1007/bf01198477
[2]
Baker, I. N. "Towers of exponents and other composite maps" Complex Variables Theory Appl. (1989) 10.1080/17476938908814364
[3]
Iteration of compact holomorphic maps on a Hilbert ball

Cho-Ho Chu, Pauline Mellon

Proceedings of the American Mathematical Society 1997 10.1090/s0002-9939-97-03761-1
[4]
Dye, J. "Random products of contractions in Banach spaces" Trans. Amer. Math. Soc. (1991) 10.2307/2001660
[5]
Dye, John M. "Unrestricted iterations of nonexpansive mappings in Banach spaces" Nonlinear Anal. (1992) 10.1016/0362-546x(92)90109-r
[6]
Earle, Clifford J. "A fixed point theorem for holomorphic mappings" (1970)
[7]
Fan, Ky "Iteration of analytic functions of operators" Math. Z. (1982) 10.1007/bf01215332
[8]
Gill, John "Complex dynamics of the limit periodic system 𝐹_{𝑛}(𝑧)=𝐹_{𝑛-1}(𝑓_{𝑛}(𝑧)),𝑓_{𝑛}→𝑓" J. Comput. Appl. Math. (1990) 10.1016/0377-0427(90)90420-5
[9]
Gill, John "Compositions of analytic functions of the form 𝐹_{𝑛}(𝑧)=𝐹_{𝑛-1}(𝑓_{𝑛}(𝑧)),𝑓_{𝑛}(𝑧)→𝑓(𝑧)" J. Comput. Appl. Math. (1988) 10.1016/0377-0427(88)90279-8
[10]
Gill, John "Inner composition of analytic mappings on the unit disk" Internat. J. Math. Math. Sci. (1991) 10.1155/s0161171291000236
[11]
Gill, John "Limit periodic iteration" Appl. Numer. Math. (1988) 10.1016/0168-9274(83)90008-9
[12]
Goebel, Kazimierz (1984)
[13]
Goebel, Kazimierz "Iterating holomorphic self-mappings of the Hilbert ball" Proc. Japan Acad. Ser. A Math. Sci. (1982)
[14]
Harris, Lawrence A. "Schwarz-Pick systems of pseudometrics for domains in normed linear spaces" (1979)
[15]
Lorentzen, Lisa "Compositions of contractions" J. Comput. Appl. Math. (1990) 10.1016/0377-0427(90)90428-3
[16]
Reich, Simeon "The alternating algorithm of von Neumann in the Hilbert ball" Dynam. Systems Appl. (1993)
[17]
Reich, Simeon "The Denjoy-Wolff theorem" Ann. Univ. Mariae Curie-Sk\l odowska Sect. A (1997)
[18]
Sine, Robert "Behavior of iterates in the Poincaré metric" Houston J. Math. (1989)
[19]
Stachura, Adam "Iterates of holomorphic self-maps of the unit ball in Hilbert space" Proc. Amer. Math. Soc. (1985) 10.2307/2044559
[20]
Suffridge, T. J. "Common fixed points of commuting holomorphic maps of the hyperball" Michigan Math. J. (1974)
[21]
Vezentini, È. "Iterations of holomorphic mappings" Uspekhi Mat. Nauk (1985)
[22]
Vesentini, Edoardo "On a theorem of Wolff and Denjoy" Rend. Sem. Mat. Fis. Milano (1983) 10.1007/bf02924880
[23]
Włodarczyk, Kazimierz "Iterations of holomorphic maps of infinite-dimensional homogeneous domains" Monatsh. Math. (1985) 10.1007/bf01304195
[24]
Włodarczyk, Kazimierz "Julia’s lemma and Wolff’s theorem for 𝐽*-algebras" Proc. Amer. Math. Soc. (1987) 10.2307/2046348
[25]
Włodarczyk, Kazimierz "Studies of iterations of holomorphic maps in 𝐽*-algebras and complex Hilbert spaces" Quart. J. Math. Oxford Ser. (2) (1986) 10.1093/qmath/37.2.245
[26]
Zhang, Wen Jun "Random iteration of holomorphic self-maps over bounded domains in 𝐂^{𝐍}" Chinese Ann. Math. Ser. B (1995)
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Citations
26
References
Details
Published
Jul 27, 2000
Vol/Issue
128(12)
Pages
3475-3482
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Cite This Article
K. Włodarczyk, D. Klim, E. Gontarek (2000). Random iterations of holomorphic maps in complex Banach spaces. Proceedings of the American Mathematical Society, 128(12), 3475-3482. https://doi.org/10.1090/s0002-9939-00-05906-2
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