Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4622583 | Journal of Mathematical Analysis and Applications | 2007 | 5 Pages |
Abstract
Let K be a weakly compact, convex subset of a Banach space X with normal structure. Browder–Kirk's theorem states that every non-expansive mapping T which maps K into K has a fixed point in K. Suppose now that WCC(X) is the collection of all non-empty weakly compact convex subsets of X. We shall define a certain weak topology Tw on WCC(X) and have the above-mentioned result extended to the hyperspace (WCC(X);Tw).
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