On generic convergence of successive approximations of mappings with convex and compact point images

DOI10.1007/s00605-022-01813-yarXiv2211.02298OpenAlexW4312185067MaRDI QIDQ6076257

Katriin Pirk, Christian Bargetz, Emir Medjic

Publication date: 23 October 2023

Published in: Monatshefte für Mathematik (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2211.02298

zbMATH Keywords

Banach spacegeneric propertysuccessive approximationsset-valued nonexpansive mapping

Mathematics Subject Classification ID

Set-valued operators (47H04) Contraction-type mappings, nonexpansive mappings, (A)-proper mappings, etc. (47H09) Fixed-point iterations (47J26)

Cites Work

• \(\sigma\)-porosity of the set of strict contractions in a space of non-expansive mappings
• Some new results on smoothness and rotundity in normed linear spaces
• Generic existence and approximation of fixed points for nonexpansive set-valued maps
• Nearly all convex bodies are smooth and strictly convex
• Porosity results for sets of strict contractions on geodesic metric spaces
• The set of noncontractive mappings is -porous in the space of all nonexpansive mappings
• A Note on Contractive Mappings
• Some logical metatheorems with applications in functional analysis
• Convex analysis in normed spaces and metric projections onto convex bodies
• Continuity of Metric Projections
• Convex Bodies and Periodic Homeomorphisms in Hilbert Space
• Porosity phenomena of non-expansive, Banach space mappings
• Generic properties of nonexpansive mappings on unbounded domains
• On successive approximations for compact-valued nonexpansive mappings
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