A Denjoy-Wolff theorem for compact holomorphic mappings in reflexive Banach spaces

DOI10.1016/J.JMAA.2012.06.044zbMath1329.32007OpenAlexW2022452487MaRDI QIDQ714061

Simeon Reich, Tadeusz Kuczumow, Budzyńska, Monika

Publication date: 19 October 2012

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2012.06.044

zbMATH Keywords

fixed pointKobayashi distancehorosphereholomorphic mappingDenjoy-Wolff theoremiterates of holomorphic mappings\(k_{D}\)-nonexpansive mapping

Mathematics Subject Classification ID

Fixed-point theorems (47H10) Infinite-dimensional holomorphy (46G20) Iteration of holomorphic maps, fixed points of holomorphic maps and related problems for several complex variables (32H50) Holomorphic functions of several complex variables (32A10) Holomorphic maps in nonlinear functional analysis (46T25)

Related Items (2)

Wolff–Denjoy theorems in geodesic spaces ⋮ Denjoy-Wolff theorems for Hilbert's and Thompson's metric spaces

Cites Work

• Theorems of Denjoy-Wolff type
• The Denjoy-Wolff theorem in \(\mathbb C^n\)
• Iterates of holomorphic and \(k_ D\)-nonexpansive mappings in convex domains in \({\mathbb{C}}^ n\)
• Horospheres and iterates of holomorpic maps
• Product formulas, nonlinear semigroups, and accretive operators
• The Denjoy-Wolff theorem in the open unit ball of a strictly convex Banach space
• The Denjoy-Wolff theorem for condensing holomorphic mappings
• Holomorphic retracts and intrinsic metrics in convex domains
• Invariant distances on complex manifolds and holomorphic mappings
• On conditions under which isometries have bounded orbits
• Iterates of Holomorphic Self-Maps of the Unit Ball in Hilbert Space
• Complex Geodesics on Convex Domains
• Invariant distances and metrics in complex analysis
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