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A Generalization of a Fixed Point Theorem of Reich

Published online by Cambridge University Press:  20 November 2018

G. E. Hardy  and
T. D. Rogers
G. E. Hardy
Affiliation:
University of Alberta, Edmonton Alberta
T. D. Rogers
Affiliation:
University of Alberta, Edmonton Alberta
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The following theorem is the principal result of this paper.

Let (M, d) be a metric space and T a self-mapping of M satisfying the condition for x,y ∊ M

1

where a, b, c, e,f are nonnegative and we set α=a+b+c+e+f.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 16 , Issue 2 , June 1973 , pp. 201 - 206
Copyright
Copyright © Canadian Mathematical Society 1973

References

1. Reich, S., Kannarf’s fixed point theorem, Bull. Univ. Mat. Italiana, (4) 4 (1971), 1–11.Google Scholar
2. Kannan, R., Some remarks on fixed points, Bull. Calcutta Math. Soc. 60 (1960), 71–76.Google Scholar
3. Edelstein, M., On fixed and periodic points under contractive mappings, London J. Math. Soc. 37 (1962), 74–79.Google Scholar
4. Rakotch, E., A note on contractive mappings, Proc. Amer. Math. Soc. 13 (1962), 459–465.Google Scholar
5. Meir, A. and Keeler, E., A theorem on contractive mappings, J. Math. Anal. Appl. 28 (1969), 26–29.Google Scholar
6. Bonsall, F. F., Lectures on some fixed point theorems of functional analysis, Tata Institute of Fundamental Research, Bombay, 1952.Google Scholar
7. Nadler, S. B., Sequences of contractions and fixed points, Pacific J. Math. 27 (1968), 579–585.Google Scholar