Halpern iteration in CAT\((\kappa)\) spaces

DOI10.1007/s10114-011-9312-7zbMath1326.47093OpenAlexW2141921641MaRDI QIDQ546290

Bozena Piatek

Publication date: 24 June 2011

Published in: Acta Mathematica Sinica. English Series (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10114-011-9312-7

zbMATH Keywords

iterative methodsmetric treesCAT\((\kappa)\) spaces

Mathematics Subject Classification ID

Iterative procedures involving nonlinear operators (47J25) Set-valued maps in general topology (54C60) Complete metric spaces (54E50) Fixed-point and coincidence theorems (topological aspects) (54H25) Contraction-type mappings, nonexpansive mappings, (A)-proper mappings, etc. (47H09)

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Cites Work

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• Viscosity approximation methods for nonexpansive multimaps in Banach spaces
• Fixed point theorems in \(\mathbb R\)-trees with applications to graph theory
• Strongly convergent approximations to fixed points of total asymptotically nonexpansive mappings
• Halpern's iteration in CAT(0) spaces
• Iterative algorithms for nonexpansive mappings on Hadamard manifolds
• CAT\((k)\)-spaces, weak convergence and fixed points
• Strong convergence theorems for resolvents of accretive operators in Banach spaces
• Approximation of fixed points of nonexpansive mappings
• Modified Mann iterations for nonexpansive semigroups in Banach space
• Iterative approximation of fixed points of nonexpansive mappings
• Reich's problem concerning Halpern's convergence
• Approximation of nearest common fixed point of nonexpansive mappings in Hilbert spaces
• Iterative Algorithms for Nonlinear Operators
• A sufficient and necessary condition for Halpern-type strong convergence to fixed points of nonexpansive mappings
• Strong convergence of approximated sequences for nonexpansive mappings in Banach spaces
• A selection theorem in metric trees
• Fixed points of nonexpanding maps

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