Hostname: page-component-cd9895bd7-8ctnn Total loading time: 0 Render date: 2024-12-26T17:49:30.452Z Has data issue: false hasContentIssue false
  • English
  • Français

A variational inequality in non-compact sets and its applications

Published online by Cambridge University Press:  17 April 2009

Won Kyu Kim  and
Kok-Keong Tan
Won Kyu Kim
Affiliation:
Department of Mathematics Education, Chungbuk National University Cheongju, 360–763, Korea
Kok-Keong Tan
Affiliation:
Department of Mathematics, Statistics and Computing Science Dalhousie University Halifax NS, CanadaB3H 3J5
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.

In this note, we shall prove a new variational inequality in non-compact sets and as an application, we prove a generalisation of the Schauder-Tychonoff fixed point theorem.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 46 , Issue 1 , August 1992 , pp. 139 - 148
Copyright
Copyright © Australian Mathematical Society 1992

References

[1]Aubin, J.P. and Ekeland, I., Applied nonlinear analysis (John Wiley and Sons, New York, 1984).Google Scholar
[2]Browder, F.E., ‘A new generalization of the Schauder fixed point theorem’, Math. Ann. 174 (1967), 285–290.CrossRefGoogle Scholar
[3]Browder, F.E., ‘The fixed point theory of multi-valued mappings in topological vector spaces’, Math. Ann. 177 (1968), 283–301.CrossRefGoogle Scholar
[4]Ding, X.P., Kim, W.K. and Tan, K.-K., ‘Equilibria of non-compact generalized games with. L*-majorized preference correspondences’, J. Math. Anal. Appl. 164 (1992), 508–517.CrossRefGoogle Scholar
[5]Halpern, B., ‘Fixed point theorems for set-valued maps in finite dimensional spaces’, Math. Ann. 189 (1970), 87–98.CrossRefGoogle Scholar
[6]Hartman, P. and Stampacchia, G., ‘On some nonlinear elliptic functional differential equations’, Acta Math. 115 (1966), 271–310.CrossRefGoogle Scholar
[7]Horvath, C., ‘Some results in a multivalued mappings and inequalities without convexity’, in Nonlinear and convex analysis: Lecture Notes in Pure and Appl. Math. Series 107 (Springer-Verlag, Berlin, Heidelberg, New York, 1987).Google Scholar
[8]Kneser, H., ‘Sur un theoreme fondamental de la theorie des jeux’, C.R. Acad. Sci. Paris 234 (1952), 2418–2420.Google Scholar
[9]Rudin, W., Functional analysis (McGraw-Hill Inc., 1973).Google Scholar
[10]Shih, M.-H. and Tan, K.-K., ‘Minimax inequalities and applications’, Contemp. Math. 54 (1986), 45–63.CrossRefGoogle Scholar
[11]Shih, M.-H. and Tan, K.-K., ‘Covering theorems of convex sets related to fixed point theorems’, in Nonlinear and convex analysis, Editors Lin, B.L. and Simons, S., pp. 235–244 (Marcel Dekker, 1987).Google Scholar
[12]Tan, K.-K., ‘Comparison theorems on minimax inequalities, variational inequalities and fixed point theorems’, J. London Math. Soc. 28 (1983), 555–562.CrossRefGoogle Scholar