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A note on the extension of contractive mappings


Author: J. L. Solomon
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
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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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DOI: https://doi.org/10.1090/S0002-9939-1973-0322784-7
Keywords: Fixed point, contractive map, contractive extension property, iterative test
Article copyright: © Copyright 1973 American Mathematical Society

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