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Some Remarks Concerning Contraction Mappings

Published online by Cambridge University Press:  20 November 2018

Simeon Reich*
Affiliation:
Israel Institute of Technology, Haifa, Israel
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The following result is proved in [1, p. 6].

Theorem 1. Let X be a complete metric space, and let T and Tn(n = 1, 2,…)be contraction mappings of X into itself with the same Lipschitz constant k<1, and with fixed points u and un respectively. Suppose that limn → ∞ Tn(x) = T(x) for every x ∊ X. Then limn → ∞ un = u.

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 1971

References

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5. Kannan, R., Some results on fixed points?II, Amer. Math. Monthly 76 (1969), 405-408.Google Scholar