Fixed points in nonconvex domains
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- by Eric Chandler and Gary Faulkner
- Proc. Amer. Math. Soc. 80 (1980), 635-638
- DOI: https://doi.org/10.1090/S0002-9939-1980-0587942-9
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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.References
- W. G. Dotson Jr., Fixed point theorems for non-expansive mappings on star-shaped subsets of Banach spaces, J. London Math. Soc. (2) 4 (1971/72), 408–410. MR 296778, DOI 10.1112/jlms/s2-4.3.408
- Ludvík Janoš, On representations of selfmappings, Proc. Amer. Math. Soc. 26 (1970), 529–533. MR 270346, DOI 10.1090/S0002-9939-1970-0270346-X
- Ludvik Janos and J. L. Solomon, A fixed point theorem and attractors, Proc. Amer. Math. Soc. 71 (1978), no. 2, 257–262. MR 482716, DOI 10.1090/S0002-9939-1978-0482716-2
- A. D. Wallace, Inverses in Euclidean mobs, Math. J. Okayama Univ. 3 (1953), 23–28. MR 62137
Bibliographic Information
- © Copyright 1980 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 80 (1980), 635-638
- MSC: Primary 47H10; Secondary 47H09
- DOI: https://doi.org/10.1090/S0002-9939-1980-0587942-9
- MathSciNet review: 587942