No CrossRef data available.
Article contents
Some remarks on the location of fixed points
Published online by Cambridge University Press: 09 April 2009
Abstract
Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.
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
- 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
You have
Access