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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
Published by: American Mathematical Society
Stable URL: http://www.jstor.org/stable/2038688
Page Count: 4
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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.
Proceedings of the American Mathematical Society © 1973 American Mathematical Society