Weak fixed point property for nonexpansive mappings with respect to orbits in Banach spaces

DOI10.1007/s11784-016-0310-3zbMath1457.47004OpenAlexW2507239879MaRDI QIDQ343891

Hamid Reza Hajisharifi, Majid Fakhar, Alireza Amini-Harandi

Publication date: 29 November 2016

Published in: Journal of Fixed Point Theory and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11784-016-0310-3

zbMATH Keywords

fixed pointBanach spaceGoebel-Karlovitz lemmaminimal invariant setsnonexpansive with respect to orbitsweak normal structure

Mathematics Subject Classification ID

Fixed-point theorems (47H10) Geometry and structure of normed linear spaces (46B20) Contraction-type mappings, nonexpansive mappings, (A)-proper mappings, etc. (47H09)

Related Items (12)

Nonexpansive Mappings, Their Extensions, and Generalizations in Banach Spaces ⋮ Approximating fixed points of a general class of nonexpansive mappings in Banach spaces with applications ⋮ On the fixed point property for orbital contractions in Banach spaces ⋮ Approximate fixed points of \(\alpha\)-nonexpansive mappings ⋮ Fixed points and common fixed points for orbit-nonexpansive mappings in metric spaces ⋮ Normal structure and orbital fixed point conditions ⋮ Fixed point results for a class of monotone nonexpansive type mappings in hyperbolic spaces ⋮ On some generalization of multivalued nonexpansive mappings ⋮ Fixed point problems for nonexpansive mappings in bounded sets of Banach spaces ⋮ Non-convex proximal pair and relatively nonexpansive maps with respect to orbits ⋮ Study of minimal invariant pairs for relatively nonexpansive mappings with respect to orbits ⋮ Unnamed Item

Cites Work

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• Generalized asymptotic pointwise contractions and nonexpansive mappings involving orbits
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• Existence of fixed points of nonexpansive mappings in a space without normal structure
• Measures of noncompactness in metric fixed point theory
• Uniformly nonsquare Banach spaces have the fixed point property for nonexpansive mappings
• Reflexivity is equivalent to the perturbed fixed point property for cascading nonexpansive maps in Banach lattices
• On the Converse of the Nonexpansive Map Fixed Point Theorem for Hilbert Space
• The failure of the fixed point property for unbounded sets in 𝑐₀
• The Fixed Point Property and Unbounded Sets in Hilbert Space
• A Fixed Point Theorem for Mappings which do not Increase Distances

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