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A Note on the Extension of Contractive Mappings

J. L. Solomon
Proceedings of the American Mathematical Society
Vol. 40, No. 1 (Sep., 1973), pp. 319-322
DOI: 10.2307/2038688
Stable URL: http://www.jstor.org/stable/2038688
Page Count: 4
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
A Note on the Extension of Contractive Mappings
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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.

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