On the removal of weak compactness arguments in proof mining

DOI10.1016/j.aim.2019.106728zbMath1446.03100arXiv1810.01508OpenAlexW2966650606MaRDI QIDQ2324564

Yanyan Li

Publication date: 11 September 2019

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

Full work available at URL: https://arxiv.org/abs/1810.01508

zbMATH Keywords

nonexpansive mappingsproof miningrates of metastabilityquantitative versionsconservation resultsbounded functional interpretation

Mathematics Subject Classification ID

Iterative procedures involving nonlinear operators (47J25) Fixed-point theorems (47H10) Contraction-type mappings, nonexpansive mappings, (A)-proper mappings, etc. (47H09) Functionals in proof theory (03F10) Second- and higher-order arithmetic and fragments (03F35) Nonlinear ergodic theorems (47H25)

Related Items (14)

Rates of asymptotic regularity for the alternating Halpern-Mann iteration ⋮ Strong Convergence for the Alternating Halpern–Mann Iteration in CAT(0) Spaces ⋮ The finitary content of sunny nonexpansive retractions ⋮ Unnamed Item ⋮ Mathematical logic: proof theory, constructive mathematics. Abstracts from the workshop held November 8--14, 2020 (hybrid meeting) ⋮ A quantitative multiparameter mean ergodic theorem ⋮ Proof-theoretic uniform boundedness and bounded collection principles and countable Heine-Borel compactness ⋮ The abstract type of the real numbers ⋮ Quantitative results on a Halpern-type proximal point algorithm ⋮ Metastability of the proximal point algorithm with multi-parameters ⋮ Quantitative translations for viscosity approximation methods in hyperbolic spaces ⋮ BOUNDS FOR INDEXES OF NILPOTENCY IN COMMUTATIVE RING THEORY: A PROOF MINING APPROACH ⋮ A Rate of Metastability for the Halpern Type Proximal Point Algorithm ⋮ On false Heine/Borel compactness principles in proof mining

Cites Work

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• On quantitative versions of theorems due to F. E. Browder and R. Wittmann
• Effective metastability of Halpern iterates in \(CAT(0)\) spaces
• Injecting uniformities into Peano arithmetic
• Approximation of fixed points of nonexpansive mappings
• The approximation of fixed points of compositions of nonexpansive mappings in Hilbert space
• Addendum to: ``Effective metastability of Halpern iterates in CAT(0) spaces
• Bounded functional interpretation
• Convergence of approximants to fixed points of nonexpansive nonlinear mappings in Banach spaces
• On the computational content of convergence proofs via Banach limits
• Effective results on nonlinear ergodic averages in CAT spaces
• ÜBER EINE BISHER NOCH NICHT BENÜTZTE ERWEITERUNG DES FINITEN STANDPUNKTES
• Rates of asymptotic regularity for Halpern iterations of nonexpansive mappings
• Strongly majorizable functionals of finite type: A model for barrecursion containing discontinuous functionals
• Some logical metatheorems with applications in functional analysis
• A Logical Uniform Boundedness Principle for Abstract Metric and Hyperbolic Spaces
• PROOF-THEORETIC METHODS IN NONLINEAR ANALYSIS
• General logical metatheorems for functional analysis
• Applied Proof Theory: Proof Interpretations and Their Use in Mathematics
• Fixed points of nonexpanding maps

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