Article ID Journal Published Year Pages File Type
4622583 Journal of Mathematical Analysis and Applications 2007 5 Pages PDF
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).

Related Topics
Physical Sciences and Engineering Mathematics Analysis