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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
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Abstract

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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

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