The finitary content of sunny nonexpansive retractions
DOI10.1142/S0219199719500937OpenAlexW2994371854WikidataQ126623363 ScholiaQ126623363MaRDI QIDQ5129245
Andrei Sipoş, Ulrich Kohlenbach
Publication date: 26 October 2020
Published in: Communications in Contemporary Mathematics (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1812.04940
metastabilityresolventsuniformly convex Banach spacesHalpern iterationproof miningfunctional interpretationuniformly smooth Banach spacessunny nonexpansive retractionspseudocontractionsBruck iteration
Nonlinear accretive operators, dissipative operators, etc. (47H06) Fixed-point theorems (47H10) Contraction-type mappings, nonexpansive mappings, (A)-proper mappings, etc. (47H09) Functionals in proof theory (03F10)
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- Fluctuations, effective learnability and metastability in analysis
- On quantitative versions of theorems due to F. E. Browder and R. Wittmann
- Logical metatheorems for abstract spaces axiomatized in positive bounded logic
- On Reich's strong convergence theorems for resolvents of accretive operators
- Strong convergence theorems for resolvents of accretive operators in Banach spaces
- Product formulas, nonlinear semigroups, and accretive operators
- Characteristic inequalities of uniformly convex and uniformly smooth Banach spaces
- Approximation of fixed points of nonexpansive mappings
- An example concerning fixed points
- On the arithmetical content of restricted forms of comprehension, choice and general uniform boundedness
- A strongly convergent iterative solution of \(0 \in U(x)\) for a maximal monotone operator U in Hilbert space
- Things that can and things that cannot be done in PRA
- Nonexpansive projections on subsets of Banach spaces
- Metamathematical investigation of intuitionistic arithmetic and analysis. With contributions by C. A. Smorynski, J. I. Zucker and W. A. Howard
- On the removal of weak compactness arguments in proof mining
- Quantitative results for Halpern iterations of nonexpansive mappings
- Approximation of zeros of accretive operators in a Banach space
- Addendum to: ``Effective metastability of Halpern iterates in CAT(0) spaces
- Bounded functional interpretation
- An explicit construction of sunny nonexpansive retractions in Banach spaces
- Convergence of approximants to fixed points of nonexpansive nonlinear mappings in Banach spaces
- Construction of fixed points of nonlinear mappings in Hilbert space
- A characterization of strict convexity of Banach spaces and other uses of duality mappings
- Uniform convexity in factor and conjugate spaces
- On the computational content of convergence proofs via Banach limits
- Effective results on nonlinear ergodic averages in CAT spaces
- Construction of sunny nonexpansive retractions in Banach spaces
- ÜBER EINE BISHER NOCH NICHT BENÜTZTE ERWEITERUNG DES FINITEN STANDPUNKTES
- Computational Problems in Metric Fixed Point Theory and their Weihrauch Degrees
- Strong and weak convergence theorems for locally nonexpansive mappings in Banach spaces
- Inequalities in Banach spaces with applications
- Differential Equations on Closed Subsets of a Banach Space
- A Characterization of Hilbert Space
- Strong convergence of approximated sequences for nonexpansive mappings in Banach spaces
- Approximate fixed point sequences and convergence theorems for Lipschitz pseudocontractive maps
- On proximal mappings with Young functions in uniformly convex Banach spaces
- Some logical metatheorems with applications in functional analysis
- PROOF-THEORETIC METHODS IN NONLINEAR ANALYSIS
- Norm convergence of multiple ergodic averages for commuting transformations
- Rate of Metastability for Bruck'S Iteration of Pseudocontractive Mappings in Hilbert Space
- General logical metatheorems for functional analysis
- Applied Proof Theory: Proof Interpretations and Their Use in Mathematics
- Stability Inequalities for Semimonotonically Perturbed Nonhomogeneous Boundary Problems
- Classes of Semi-Inner-Product Spaces
- Fixed points of nonexpanding maps
- Nonlinear mappings of nonexpansive and accretive type in Banach spaces
- Nonexpansive retracts of Banach spaces
- The construction of an asymptotic center with a fixed-point property
- On n-quantifier induction
- Properties of Fixed-Point Sets of Nonexpansive Mappings in Banach Spaces
- On the Interpretation of Non-Finitist Proofs--Part I
- On the interpretation of non-finitist proofs–Part II
- On uniformly convex functions