On the existence of fixed points for typical nonexpansive mappings on spaces with positive curvature

DOI10.12775/TMNA.2020.040zbMath1491.47041arXiv2004.02567OpenAlexW3111267329MaRDI QIDQ2240537

Michael Dymond, Simeon Reich, Emir Medjic, Christian Bargetz

Publication date: 4 November 2021

Published in: Topological Methods in Nonlinear Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2004.02567

zbMATH Keywords

nonexpansive mappings\(\sigma\)-porous setsRakotch contractionsspaces of positive curvature

Mathematics Subject Classification ID

Baire category, Baire spaces (54E52) Contraction-type mappings, nonexpansive mappings, (A)-proper mappings, etc. (47H09) Special maps on metric spaces (54E40)

Related Items (5)

Sufficient conditions for perturbations to define the resolvent of the equilibrium problem on complete geodesic spaces ⋮ Convergence of the Cimmino algorithm for common fixed point problems with a countable family of operators ⋮ Porosity phenomena of non-expansive, Banach space mappings ⋮ Generic properties of nonexpansive mappings on unbounded domains ⋮ Unnamed Item

Cites Work

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• \(\sigma\)-porosity of the set of strict contractions in a space of non-expansive mappings
• Two porosity theorems for nonexpansive mappings in hyperbolic spaces
• Mann's algorithm for nonexpansive mappings in CAT\((\kappa)\) spaces
• The fixed point property and unbounded sets in spaces of negative curvature
• CAT\((k)\)-spaces, weak convergence and fixed points
• Porosity results for sets of strict contractions on geodesic metric spaces
• On \(\sigma\)-porous sets in abstract spaces
• An extension of Tietze's theorem
• The set of noncontractive mappings is -porous in the space of all nonexpansive mappings
• A Note on Contractive Mappings
• Nonexpansive iterations in hyperbolic spaces
• Spheres in Infinite-Dimensional Normed Spaces are Lipschitz Contractible
• FIXED-POINT THEOREMS FOR NONCOMPACT MAPPINGS IN HILBERT SPACE

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