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Sequences of Contractions in a Generalized Metric Space
Published online by Cambridge University Press: 20 November 2018
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The main aim of this paper is to study the convergence of a sequence of contractions in a generalized metric space. More specifically, we investigate the following question:
"If a sequence of contractions {fr} with fixed points ur (r = 1,2,...) converges to a mapping f with a fixed point u, under what conditions will the sequence ur converge to u?"
A partial answer to the above question has been given in metric spaces by Bonsall [1]. This result has since been improved by Russell and Singh [6]. Further results will now be given in a generalized metric space.
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- Research Article
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- Copyright © Canadian Mathematical Society 1970
References
1.
Bonsall, F., Lecture notes on some fixed point theorems in analysis, Tata Institute of Fundamental Research, Bombay, India, 1962.Google Scholar
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Diaz, and Margolis, , A fixed point theorem of the alternative for contractions on a generalized complete metric space, Bull. Amer. Math. Soc.
74, No. 2 (1968), 305-309.Google Scholar
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Luxemburg, W. A. J., On the convergence of successive approximations in the theory of ordinary differential equations, II, Nederl. Akad. Wetensch. Proc. (ser. A61) Indag. Mathematicae
20 (1958), 540-546.Google Scholar
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Luxemburg, W. A. J., On the convergence of successive approximations in the theory of ordinary differential equations III, Nieuw Archief Voor Wiskunde
6, No. 3 (1958), 93-98.Google Scholar
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Russel, and Singh, , A remark on a fixed point theorem for contractions, Canad. Math. Bull, (to appear).Google Scholar
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