A note on the extension of contractive mappings
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- by J. L. Solomon PDF
- Proc. Amer. Math. Soc. 40 (1973), 319-322 Request permission
Abstract:
In this note a question posed by J. D. Bryant and L. F. Guseman, Jr. is answered. It is shown that for dense subsets of finite dimensional Banach spaces, the iterative test being conclusive and the contractive extension property are not equivalent. If $(X,d)$ is a complete locally compact and chainable-metric space, a characterization of these dense subsets for which the iterative test is conclusive is given.References
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Jack Bryant and L. F. Guseman, Jr., Extensions of contractive mappings and Edelstein’s iterative test, Canad. Math. Bull. (to appear).
- 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
- P. R. Meyers, Minimum number of subsets to distinguish individual elements, J. Res. Nat. Bur. Standards Sect. B 71B (1967), 21–22. MR 210604
- Sam B. Nadler Jr., A note on an iterative test of Edelstein, Canad. Math. Bull. 15 (1972), 381–386. MR 312483, DOI 10.4153/CMB-1972-070-7
Additional Information
- © Copyright 1973 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 40 (1973), 319-322
- MSC: Primary 54C20; Secondary 54H25
- DOI: https://doi.org/10.1090/S0002-9939-1973-0322784-7
- MathSciNet review: 0322784