Hostname: page-component-78c5997874-ndw9j Total loading time: 0 Render date: 2024-11-20T01:26:40.085Z Has data issue: false hasContentIssue false
  • English
  • Français

A selection theorem and its applications

Published online by Cambridge University Press:  17 April 2009

Xie Ping Ding ,
Won Kyu Kim  and
Kok-Keong Tan
Xie Ping Ding
Affiliation:
Department of Mathematics Sichuan Normal, University Chengdu, Sichuan, China
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 paper, we first prove an improved version of the selection theorem of Yannelis-Prabhakar and next prove a fixed point theorem in a non-compact product space. As applications, an intersection theorem and two equilibrium existence theorems for a non-compact abstract economy are given.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 46 , Issue 2 , October 1992 , pp. 205 - 212
Copyright
Copyright © Australian Mathematical Society 1992

References

[1]Borglin, A. and Keiding, H., ‘Existence of equilibrium actions and of equilibrium: a note on the ‘new’ existence theorem’, J. Math. Econom. 3 (1976), 313–316.CrossRefGoogle Scholar
[2]Browder, F.E., ‘The fixed point theory of multi-valued mappings in topological vector spaces’, Math. Ann. 177 (1968), 283–301.CrossRefGoogle Scholar
[3]Cullen, H.F., Introduction to general topology (D. C. Heath, Boston, 1968).Google Scholar
[4]Dugundji, J., Topology (Allyn and Bacon, Inc., Boston, 1966).Google Scholar
[5]Fan, K., ‘Fixed-point and minimax theorems in locally convex topological linear spaces’, Proc. Nat. Acad. Sci. U.S.A. 38 (1952), 131–136.CrossRefGoogle ScholarPubMed
[6]Fan, K., ‘Sur un théorème minimax’, C.R. Acad. Sci. Paris Ser. 1 259 (1964), 3925–3928.Google Scholar
[7]Fan, K., ‘A minimax inequality and applications’, in Inequalities III, Editor Shisha, O. (Academic Press, New York, 1972).Google Scholar
[8]Himmelberg, C.J., ‘Fixed points of compact multifunctions’, J. Math. Anal. Appl. 38 (1972), 205–207.CrossRefGoogle Scholar
[9]Lassonde, M., ‘Fixed point for Kakutani factorizable multifunctions’, J. Math. Anal. Appl. 152 (1990), 46–60.CrossRefGoogle Scholar
[10]Michael, E., ‘A note on paracompact spaces’, Proc. Amer. Math. Soc. 4 (1953), 831–838.CrossRefGoogle Scholar
[11]Shafer, W. and Sonnenschein, H., ‘Equilibrium in abstract economies without ordered preferences’, J. Math. Econom. 2 (1975), 345–348.CrossRefGoogle Scholar
[12]Shih, M.H. and Tan, K.-K., ‘Non-compact sets with convex sections’, Pacific J. Math. 119 (1985), 473–479.CrossRefGoogle Scholar
[13]Smart, D.R., Fixed point theorems (Cambridge University Press, Cambridge, MA, 1974).Google Scholar
[14]Tarafdar, E., ‘A fixed point theorem and equilibrium point of an abstract economy’, J. Math. Econom. 20 (1991), 211–218.CrossRefGoogle Scholar
[15]Yannelis, N.C. and Prabhakar, N.D., ‘Existence of maximal elements and equilibria in linear topological spaces’, J. Math. Econom. 12 (1983), 233–245.CrossRefGoogle Scholar