This paper is concerned with weak uniform normal structure and iterative fixed points of nonexpansive mappings. Precisely, in Section 1, we show that the geometrical coefficient β(X) for a Banach space X recently introduced by Jimenez-Melado [8] is exactly the weakly convergent sequence coefficient WCS(X) introduced by Bynum [1] in 1980. We then show in Section 2 that all kinds of James' quasi-reflexive spaces have weak uniform normal structure. Finally, in Section 3, we show that in a space X with weak uniform normal structure, every nonexpansive self-mapping defined on a weakly sequentially compact convex subset of X admits an iterative fixed point.
@article{bwmeta1.element.bwnjournal-article-cmv68i1p17bwm,
author = {Dom\'\i nguez Benavides, T. and L\'opez Acedo, G. and Xu, Hong},
title = {Weak uniform normal structure and iterative fixed points of nonexpansive mappings},
journal = {Colloquium Mathematicae},
volume = {68},
year = {1995},
pages = {17-23},
zbl = {0845.46006},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-cmv68i1p17bwm}
}
Domínguez Benavides, T.; López Acedo, G.; Xu, Hong. Weak uniform normal structure and iterative fixed points of nonexpansive mappings. Colloquium Mathematicae, Tome 68 (1995) pp. 17-23. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-cmv68i1p17bwm/
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