Fixed points for non-expansive set-valued mappings
Abstract
Let E be a Banach space and F : E --> E be a 1-Lipschitz set-valued mapping with closed convex non-empty values. We study the set of fixed points Fix(F)={ x in E : x in F(x)} and provide in any space E with dim(E) > 2 an example of such a mapping F such that Fix(F) is not connected.
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