Nonexpansive mappings on compact subsets of metric linear spaces
HTML articles powered by AMS MathViewer
- by L. F. Guseman and B. C. Peters PDF
- Proc. Amer. Math. Soc. 47 (1975), 383-386 Request permission
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
- 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
- W. G. Dotson Jr., On fixed points of nonexpansive mappings in nonconvex sets, Proc. Amer. Math. Soc. 38 (1973), 155–156. MR 313894, DOI 10.1090/S0002-9939-1973-0313894-9
- M. Edelstein, On fixed and periodic points under contractive mappings, J. London Math. Soc. 37 (1962), 74–79. MR 133102, DOI 10.1112/jlms/s1-37.1.74
- Helmut H. Schaefer, Topological vector spaces, The Macmillan Company, New York; Collier Macmillan Ltd., London, 1966. MR 0193469
- D. R. Smart, A fixed-point theorem, Proc. Cambridge Philos. Soc. 57 (1961), 430. MR 117709
Additional Information
- © Copyright 1975 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 47 (1975), 383-386
- DOI: https://doi.org/10.1090/S0002-9939-1975-0353072-2
- MathSciNet review: 0353072