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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Fixed points in nonconvex domains


Authors: Eric Chandler and Gary Faulkner
Journal: Proc. Amer. Math. Soc. 80 (1980), 635-638
MSC: Primary 47H10; Secondary 47H09
MathSciNet review: 587942
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Abstract: A lemma of Janos is used to prove that nonexpansive self-maps which ``shrink'' a compact set X away from its boundary in $ \overline {{\text{co}}} \;X$ have fixed points in X. The lemma is further employed to derive a version, for nonexpansive maps on star-shaped sets, of Janos and Solomon's fixed-point theorem for continuous maps on spaces having an attractor for compact sets.


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DOI: https://doi.org/10.1090/S0002-9939-1980-0587942-9
Keywords: Fixed points, nonexpansive mappings, retractions, strictly convex spaces
Article copyright: © Copyright 1980 American Mathematical Society