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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ap76-3-2,
author = {Eun Suk Kim and W. A. Kirk},
title = {A note on Picard iterates of nonexpansive mappings},
journal = {Annales Polonici Mathematici},
volume = {77},
year = {2001},
pages = {189-196},
zbl = {0973.47040},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap76-3-2}
}
Eun Suk Kim; W. A. Kirk. A note on Picard iterates of nonexpansive mappings. Annales Polonici Mathematici, Tome 77 (2001) pp. 189-196. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap76-3-2/