Displaying similar documents to “On locally nonexpansive mappings and local isometries”

A fixed point theorem for nonexpansive compact self-mapping

T. D. Narang (2014)

Annales UMCS, Mathematica

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A mapping T from a topological space X to a topological space Y is said to be compact if T(X) is contained in a compact subset of Y . The aim of this paper is to prove the existence of fixed points of a nonexpansive compact self-mapping defined on a closed subset having a contractive jointly continuous family when the underlying space is a metric space. The proved result generalizes and extends several known results on the subject

A note on Picard iterates of nonexpansive mappings

Eun Suk Kim, W. A. Kirk (2001)

Annales Polonici Mathematici

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Let X be a Banach space, C a closed subset of X, and T:C → C a nonexpansive mapping. It has recently been shown that if X is reflexive and locally uniformly convex and if the fixed point set F(T) of T has nonempty interior then the Picard iterates of the mapping T always converge to a point of F(T). In this paper it is shown that if T is assumed to be asymptotically regular, this condition can be weakened much further. Finally, some observations are made about the geometric conditions...