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An approach to fixed-point theorems on uniform spaces

Author: E. Tarafdar
Journal: Trans. Amer. Math. Soc. 191 (1974), 209-225
MSC: Primary 54H25; Secondary 47H10
MathSciNet review: 0362283
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Abstract: Diaz and Metcalf [2] have some interesting results on the set of successive approximations of a self mapping which is either a nonexpansion or a contraction on a metric space with respect to the set of fixed points of the mapping. We have extended most of these results to a Hausdorff uniform space. We have also proved a Banach's contraction mapping principle on a complete Hausdorff uniform space and indicated some applications in locally convex linear topological spaces.

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Keywords: Uniform space, locally convex linear topological space, family of pseudometrics, family of seminorms, nonexpansion, contraction, asymptotically regular maps, contraction mapping principle, starshaped subset
Article copyright: © Copyright 1974 American Mathematical Society

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