Hostname: page-component-586b7cd67f-t7fkt Total loading time: 0 Render date: 2024-11-24T15:31:15.505Z Has data issue: false hasContentIssue false
  • English
  • Français

A Set-Valued Generalization of Fan's Best Approximation Theorem

Published online by Cambridge University Press:  20 November 2018

Xie Ping Ding  and
Kok-Keong Tan
Xie Ping Ding
Affiliation:
Department of Mathematics, Sichuan Normal University, Chengdu, Sichuan, China
Kok-Keong Tan
Affiliation:
Department of Mathematics, Statistics and Computing Science Dalhousie University, Halifax, Nova Scotia, 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.

Let (E, T) be a Hausdorff topological vector space whose topological dual separates points of E, X be a non-empty weakly compact convex subset of E and W be the relative weak topology on X. If F: (X, W) → 2(E,T) is continuous (respectively, upper semi-continuous if £ is locally convex), approximation and fixed point theorems are obtained which generalize the corresponding results of Fan, Park, Reich and Sehgal-Singh-Smithson (respectively, Ha, Reich, Park, Browder and Fan) in several aspects.

Keywords

Primary: 47H1054C6054H25
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 44 , Issue 4 , 01 August 1992 , pp. 784 - 796
Copyright
Copyright © Canadian Mathematical Society 1992

References

1. Aubin, J.P., Mathematical Methods of Game and Economic Theory, Revised Edition, North-Holland, Amsterdam/ New York/Oxford, 1982.Google Scholar
2. Browder, F.E., On a sharpened form of the Schauder fixed point theorem, Proc. Nat. Acad. Sci. U.S.A. 74 (1977), 4749–4751.Google Scholar
3. Ding, X.P. and Tan, K.K., A minimax inequality with applications to existence of equilibrium point and fixed point theorems, Colloquium Math, to appear.Google Scholar
4. Fan, K., A generalization of Tychonoff's fixed point theorem, Math. Ann. 142 (1961), 305–310.Google Scholar
5. Fan, K., Extensions of two fixed point theorems of Browder F.E., Math. Z. 112 (1969), 234–240.Google Scholar
6. Fan, K., Some properties of convex sets related to fixed point theorems, Math. Ann. 226 (1984), 519–537.Google Scholar
7. Ha, C.W., On a minimax inequality of Ky Fan, Proc. Amer. Math. Soc. 99 (1987), 680–682.Google Scholar
8. Lin, T.C., A note on a theorem of Ky Fan, Canad. Math. Bull. 22 (1979), 513–515.Google Scholar