Fixed point theory and nonexpansive mappings

DOI10.1007/s40065-012-0042-1zbMath1267.46025OpenAlexW2042502359WikidataQ59292046 ScholiaQ59292046MaRDI QIDQ1927943

Pei-Kee Lin

Publication date: 2 January 2013

Published in: Arabian Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s40065-012-0042-1

zbMATH Keywords

weak fixed point propertyfixed point propertyultraproductBanach-Mazur distance\(E\)-convex Banach space

Mathematics Subject Classification ID

Problem books (00A07) Fixed-point theorems (47H10) Geometry and structure of normed linear spaces (46B20) Contraction-type mappings, nonexpansive mappings, (A)-proper mappings, etc. (47H09) Ultraproduct techniques in Banach space theory (46B08)

Cites Work

• The fixed point property via dual space properties
• Unconditional bases and fixed points of nonexpansive mappings
• Equivalent norms on spaces of bounded functions
• Nonstandard methods in fixed point theory
• Existence of fixed points of nonexpansive mappings in a space without normal structure
• Opial modulus and stability of the fixed point property
• There is an equivalent norm on \(\ell_1\) that has the fixed point property
• Uniformly nonsquare Banach spaces have the fixed point property for nonexpansive mappings
• A renorming of some nonseparable Banach spaces with the fixed point property
• The fixed point property under renorming in some classes of Banach spaces
• Remarks on the fixed point problem for nonexpansive maps
• Subspaces of certain Banach Sequence Spaces
• A Fixed Point Free Nonexpansive Map
• Convexity conditions in normed linear spaces.
• On one generalization of weakly compactly generated Banach spaces
• Stability of the fixed point property of Hilbert spaces
• Stability of the fixed point property in Hilbert spaces
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