Hostname: page-component-7479d7b7d-c9gpj Total loading time: 0 Render date: 2024-07-13T15:51:31.386Z Has data issue: false hasContentIssue false
  • English
  • Français

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.
Rights & Permissions [Opens in a new window]

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.

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

Brezis, H. (1968), ‘Equations et inequations nonlineaires dans les espaces vectoriels en dualit’, Ann. Inst. Fourier (Grenoble) 18, 115–175.CrossRefGoogle Scholar
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
Browder, F. (1968), ‘The fixed point theory of multi-valuerd mappings in topological vector spaces’, Math. Annalen 177, 177–283.CrossRefGoogle Scholar
Fan, K. (1961), ‘A generalization of Tychonoff's fixed point theorem’, Math. Ann. 142, 305–310.CrossRefGoogle Scholar
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