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Some remarks on the location of fixed points

Part of: Nonlinear operators and their properties

Published online by Cambridge University Press:  09 April 2009

Michael Edelstein  and
Daryl Tingley
Michael Edelstein
Affiliation:
Department of Mathematics, Statistics and Computing Science Dalhousie UniversityHalifax, N. S. B3H 4H8, Canada
Daryl Tingley
Affiliation:
Department of Mathematics, Statistics and Computing Science Dalhousie UniversityHalifax, N. S. B3H 4H8, Canada
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Abstract

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Several procedures for locating fixed points of nonexpansive selfmaps of a weakly compact convex subset of a Banach space are presented. Some of the results involve the notion of an asymptotic center or a Chebyshev center.

MSC classification

Secondary: 47H09: Contraction-type mappings, nonexpansive mappings, $A$-proper mappings, etc. 47H10: Fixed-point theorems
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 37 , Issue 3 , December 1984 , pp. 358 - 365
Copyright
Copyright © Australian Mathematical Society 1984

References

[1]Browder, F. E. and Petryshyn, W. V., ‘The solution by iteration of nonlinear functional equations in Banach spaces’, Bull. Amer. Math. Soc. 72 (1966), 571–575.CrossRefGoogle Scholar
[2]Day, M. M., James, R. C. and Swaminathan, S., ‘Normed linear spaces that are uniformly convex in every direction’, Canad. J. Math 23 (1971), 1051–1059.CrossRefGoogle Scholar
[3]Edelstein, M., ‘The construction of an asymptotic center with a fixed point property’, Bull. Amer. Math. Soc. 78 (1972), 206–208.CrossRefGoogle Scholar
[4]Edelstein, M., ‘Fixed point theorems in uniformly convex Banach spaces’, Proc. Amer. Math. Soc. 44 (1974), 369–374.Google Scholar
[5]Edelstein, M. and O'Brien, R. C., ‘Nonexpansive mappings, asymptotic regularity, and successive approximations’, J. London Math. Soc. (2) 17 (1978), 547–554.Google Scholar
[6]Floret, Klaus, ‘Eine Bemerkung über a-priori-Fixpunkte nichtexpansiver Abbildungen’, Manuscripta Math. 6 (1972), 321–326.CrossRefGoogle Scholar
[7]Kirk, W. A., ‘A fixed point theorem for mappings which do not increase distances’, Amer. Math. Monthly 72 (1965), 1004–1006.Google Scholar
[8]Lim, T. C., ‘Characterizations of normal structure’, Proc. Amer. Math. Soc. 43 (1974), 313–319.CrossRefGoogle Scholar
[9]Reinermann, J. and Shoenberg, R., ‘Some results in the fixed point theory of nonexpnsive mappings and generalized contractions’, Proc. Sem. Fixed Point Theory and its Applications, Dalhousie University, Halifax, N. S., Canada, 1975 (Academic Press).Google Scholar