Effective metastability of Halpern iterates in \(CAT(0)\) spaces

DOI10.1016/j.aim.2012.06.028zbMath1270.47060arXiv1107.3215OpenAlexW2963106285MaRDI QIDQ715208

Laurenţiu Leuştean, Ulrich Kohlenbach

Publication date: 2 November 2012

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1107.3215

zbMATH Keywords

metastabilityCAT(0) spacesnonexpansive mappingsBanach limitsproof miningHalpern iterations

Mathematics Subject Classification ID

Iterative procedures involving nonlinear operators (47J25) Fixed-point and coincidence theorems (topological aspects) (54H25) Contraction-type mappings, nonexpansive mappings, (A)-proper mappings, etc. (47H09) Global geometric and topological methods (à la Gromov); differential geometric analysis on metric spaces (53C23) Functionals in proof theory (03F10)

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Cites Work

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• Effective metastability for modified Halpern iterations in CAT(0) spaces
• On quantitative versions of theorems due to F. E. Browder and R. Wittmann
• Hopf's ergodic theorem for nonlinear operators
• Halpern's iteration in CAT(0) spaces
• Strong convergence theorems for resolvents of accretive operators in Banach spaces
• Approximation of fixed points of nonexpansive mappings
• Almost convergence and nonlinear ergodic theorems
• Iterative approximation of fixed points of nonexpansive mappings
• Approximation of common fixed points of a countable family of nonexpansive mappings in a Banach space
• On \(\Delta\)-convergence theorems in CAT\((0)\) spaces
• Reich's problem concerning Halpern's convergence
• Strongly uniform bounds from semi-constructive proofs
• Convergence of approximants to fixed points of nonexpansive nonlinear mappings in Banach spaces
• Reductive groups over a local field
• A contribution to the theory of divergent sequences
• On the computational content of convergence proofs via Banach limits
• Iteration processes for nonexpansive mappings
• Iterative Algorithms for Nonlinear Operators
• A convexity in metric space and nonexpansive mappings. I.
• ÜBER EINE BISHER NOCH NICHT BENÜTZTE ERWEITERUNG DES FINITEN STANDPUNKTES
• Some problems and results in fixed point theory
• Nonexpansive iterations in hyperbolic spaces
• Local stability of ergodic averages
• A sufficient and necessary condition for Halpern-type strong convergence to fixed points of nonexpansive mappings
• Rates of asymptotic regularity for Halpern iterations of nonexpansive mappings
• A quantitative mean ergodic theorem for uniformly convex Banach spaces
• Strong convergence of approximated sequences for nonexpansive mappings in Banach spaces
• Krasnoselskii's iteration process in hyperbolic space
• Some logical metatheorems with applications in functional analysis
• Square functions in ergodic theory
• Norm convergence of multiple ergodic averages for commuting transformations
• General logical metatheorems for functional analysis
• Applied Proof Theory: Proof Interpretations and Their Use in Mathematics
• The solution by iteration of nonlinear functional equations in Banach spaces
• Banach Limits
• Fixed points of nonexpanding maps
• On the Interpretation of Non-Finitist Proofs--Part I
• On the interpretation of non-finitist proofs–Part II

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