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A note on Picard iterates of nonexpansive mappings

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

Annales Polonici Mathematici

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 imposed.

A Note on the Measure of Solvability

D. Caponetti, G. Trombetta (2004)

Bulletin of the Polish Academy of Sciences. Mathematics

Let X be an infinite-dimensional Banach space. The measure of solvability ν(I) of the identity operator I is equal to 1.

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