Averaged mappings in the Hilbert ball

DOI10.1016/0022-247X(85)90187-8zbMath0588.47061MaRDI QIDQ1073328

Simeon Reich

Publication date: 1985

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

zbMATH Keywords

fixed pointsiterative schemesasymptotic techniquesaveraged mappings of the unit Hilbert ballellipsoid-invariance

Mathematics Subject Classification ID

Fixed-point theorems (47H10) Contraction-type mappings, nonexpansive mappings, (A)-proper mappings, etc. (47H09) Inner product spaces and their generalizations, Hilbert spaces (46C99)

Related Items

The behavior of fixed point free nonexpansive mappings in geodesic spaces ⋮ Perturbed projections and subgradient projections for the multiple-sets split feasibility problem ⋮ Coaccretive operators and firmly nonexpansive mappings in the Hilbert ball ⋮ Isometers in the Cartesian product of n unit open Hilbert balls with hyperbolic metric ⋮ Asymptotic behavior of averaged and firmly nonexpansive mappings in geodesic spaces ⋮ Convergence rate analysis for fixed-point iterations of generalized averaged nonexpansive operators ⋮ Remark on the Yosida approximation iterative technique for split monotone Yosida variational inclusions ⋮ On split monotone variational inclusion problem with multiple output sets with fixed point constraints ⋮ Split monotone variational inclusions ⋮ The Denjoy-Wolff theorem in \(\mathbb C^n\) ⋮ Projection and proximal point methods: Convergence results and counterexamples. ⋮ The asymptotic behavior of a class of nonlinear semigroups in the Hilbert ball ⋮ Around averaged mappings ⋮ Minimal Displacement of Points Under Holomorphic Mappings and Fixed Point Properties for Unions of Convex Sets ⋮ Hyperbolic monotonicity in the Hilbert ball ⋮ Nonexpansive iterations in hyperbolic spaces ⋮ Denjoy-Wolff theorems for Hilbert's and Thompson's metric spaces ⋮ Fixed point theorems for asymptotically regular mappings in modular and metric spaces ⋮ Weak Convergence of Orbits of Nonlinear Operators in Reflexive Banach Spaces ⋮ The Asymptotic Behavior of Firmly Nonexpansive Mappings ⋮ The Denjoy-Wolff theorem in the open unit ball of a strictly convex Banach space ⋮ The existence and non-existence of common fixed points for commuting families of holomorphic mappings ⋮ The Denjoy-Wolff theorem for condensing holomorphic mappings

Cites Work

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• The Dirichlet problem at infinity for a negatively curved manifold
• The asymptotics of nonexpansive iterations
• Iterating holomorphic self-mappings of the Hilbert ball
• Weak convergence theorems for nonexpansive mappings in Banach spaces
• On the asymptotic behavior of nonlinear semigroups and the range of accretive operators
• An example concerning fixed points
• Fixed points and invariant domains of holomorphic mappings of the Hilbert ball
• Uniform convexity of the hyperbolic metric and fixed points of holomorphic mappings in the Hilbert ball
• Krasnoselskii's iteration process in hyperbolic space