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Fixed points and boundaries

Name: Fixed points and boundaries
Creator: Eric Chandler
Keywords: Fixed-point theorems, fixed points, 4. Education, Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc., 0101 mathematics, boundaries, 01 natural sciences

descriptionPublicationkeyboard_double_arrow_right Article , Other literature type 01 Jul 1981 English Publisher:American Mathematical Society (AMS)Journal:Proceedings of the American Mathematical Society, volume 82, pages 398-400 (issn: 0002-9939, eissn: 1088-6826,

Authors: Eric Chandler;

doi: 10.1090/s0002-9939-1981-0612728-7 , 10.2307/2043949

Fixed points and boundaries

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Abstract

A lemma of Ludvik Janos is used to show that if a nonexpansive self-map T T of a compact set X X is contractive on Δ ′ X \Delta ’X , the boundary of X X in co ¯ X \overline {{\text {co}}} X , then T T has a fixed point in X X . It is further proven that if T ( Δ ′ X ) ∩ Δ ′ X = ∅ T(\Delta ’X) \cap \Delta ’X = \emptyset , or if T T maps any point y y of X X away from Δ ′ X \Delta ’X , then T T has a fixed point in X X .

Keywords

Fixed-point theorems, fixed points, Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc., boundaries

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