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Fixed Point Theorems for Point-to-Set Mappings

Published online by Cambridge University Press:  20 November 2018

Chi Song Wong
Chi Song Wong*
Affiliation:
Department of Mathematics, University of Windsor, Windsor, Ontario, Canada
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Abstract

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Let (X, d) be a metric space. Let Xc be the family of all non-empty closed subsets of X endowed with the Hausdorff metric D induced by d. Let f be a non-expansive mapping of X into Xc (D(f(x), f(y))≤d(x, y) for all x, y in X). Some fixed point theorems are obtained by imposing certain conditions on f and X.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 17 , Issue 4 , 01 December 1974 , pp. 581 - 586
Copyright
Copyright © Canadian Mathematical Society 1974

References

1. Belluce, L.P. and Kirk, W.A., Nonexpansive mappings and fixed points in Banach spaces, Illinois J. Math. 11 (1967), 474-479.Google Scholar
2. Belluce, L.P. and Kirk, W.A., Fixed point theorems for certain classes of nonexpansive mappings, Proc. Amer. Math. Soc. 20 (1969), 141-146.Google Scholar
3. Blumenthal, L.E., Theory and application of distance geometry, Clarendon Press, Oxford, 1953.Google Scholar
4. Boyd, D.W. and Wong, J. S. W., On nonlinear contractions, Proc. Amer. Math. Soc. 20 (1969), 458-464.Google Scholar
5. Browder, F.E., Nonexpansive nonlinear operators in a Banach space, Proc. Nat. Acad. Sci. 54 (1965), 1041-1044.Google Scholar
6. Browder, F.E., On the successive approximations for nonlinear functional equations, Proc. Kon. Nederl. Akad. Wetensch. Amsterdam A71 (1968), 27-35.Google Scholar
7. Fraser, R. B. Jr, and Nadler, Sam B. Jr.,Sequences of contractive maps and fixed points, Pacific J. Math. 31 (1969), 659-667.Google Scholar
8. Ernest, Michael, Topologies on spaces of subsets, Trans. Amer. Math. Soc. 70 (1951), 152- 182.Google Scholar
9. Chi Song, Wong, Fixed point theorems for nonexpansive mappings, J. Math. Anal. Applic. 37 (1972), 142-150.Google Scholar