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On Ky Fan's minimax principle

Part of: Nonlinear operators and their properties

Published online by Cambridge University Press:  09 April 2009

E. Tarafdar  and
H. B. Thompson
E. Tarafdar
Affiliation:
Department of Mathematics, University of Queensland, St. Lucia. Queensland 4067, Australia.
H. B. Thompson
Affiliation:
Department of Mathematics, University of Queensland, St. Lucia. Queensland 4067, Australia.
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Abstract

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A generalized version of the Knaster-Kuratowski-Mazurkiewicz theorem is obtained and used to generalize Ky Fan's minimax principle. This result is applied to a variational inequality.

MSC classification

Secondary: 47H05: Monotone operators and generalizations 47H10: Fixed-point theorems
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 26 , Issue 2 , September 1978 , pp. 220 - 226
Copyright
Copyright © Australian Mathematical Society 1978

References

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Brezis, H., Nirenberg, L., and Stampacchia, G. (1972), ‘A remark on Ky Fan's Minimax principle’, Bollenino U. M. Italiana (4) 6 293–300.Google Scholar
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Fan, K. (1972), ‘A minimax inequality and applications’, Inequalities III, edited Shisha, O. (Academic Press).Google Scholar
Knaster, B., Kuratowski, C., and Mazurkiewicz, S. (1929), ‘Ein Beweis des Fixpunktsatzes fur n-dimensionale Simplexe’, Fund. Math. 14, 132–137.CrossRefGoogle Scholar