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Proceedings of the American Mathematical Society

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

 
 

 

Nonexpansive mappings on compact subsets of metric linear spaces


Authors: L. F. Guseman and B. C. Peters
Journal: Proc. Amer. Math. Soc. 47 (1975), 383-386
DOI: https://doi.org/10.1090/S0002-9939-1975-0353072-2
MathSciNet review: 0353072
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Abstract | References | Additional Information

Abstract: Results are presented concerning the existence of fixed points of nonexpansive selfmaps on a compact starshaped subset of a metric linear space. The results are based on a general argument of D. R. Smart and extend recent results of W. G. Dotson, Jr.


References [Enhancements On Off] (What's this?)

  • [1] 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 45 #5837. MR 0296778 (45:5837)
  • [2] -, On fixed points of nonexpansive mappings in nonconvex sets, Proc. Amer. Math. Soc. 38 (1973), 155-156. MR 47 #2446. MR 0313894 (47:2446)
  • [3] M. Edelstein, On fixed and periodic points under contractive mappings, J. London Math. Soc. 37 (1962), 74-79. MR 24 #A2936. MR 0133102 (24:A2936)
  • [4] H. H. Schaefer, Topological vector spaces, Macmillan, New York, 1966. MR 33 #1689. MR 0193469 (33:1689)
  • [5] D. R. Smart, A fixed-point theorem, Proc. Cambridge Philos. Soc. 57 (1961), 430. MR 22 #8484. MR 0117709 (22:8484)


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1975-0353072-2
Keywords: Nonexpansive mappings, fixed points, starshaped sets, metric linear spaces
Article copyright: © Copyright 1975 American Mathematical Society

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