Weak uniform normal structure and iterative fixed points of nonexpansive mappings
Colloquium Mathematicum, Tome 68 (1995) no. 1, pp. 17-23
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.
Keywords:
nonexpansive mapping, iterative fixed point, geometrical coefficients of Banach spaces, James' quasi-reflexive space, weak uniform normal structure
@article{10_4064_cm_68_1_17_23,
author = {T. Dom{\'\i}nguez Benavides and G. L\'opez Acedo and Hong Xu},
title = {Weak uniform normal structure and iterative fixed points of nonexpansive mappings},
journal = {Colloquium Mathematicum},
pages = {17--23},
year = {1995},
volume = {68},
number = {1},
doi = {10.4064/cm-68-1-17-23},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/cm-68-1-17-23/}
}
TY - JOUR AU - T. Domínguez Benavides AU - G. López Acedo AU - Hong Xu TI - Weak uniform normal structure and iterative fixed points of nonexpansive mappings JO - Colloquium Mathematicum PY - 1995 SP - 17 EP - 23 VL - 68 IS - 1 UR - http://geodesic.mathdoc.fr/articles/10.4064/cm-68-1-17-23/ DO - 10.4064/cm-68-1-17-23 LA - en ID - 10_4064_cm_68_1_17_23 ER -
%0 Journal Article %A T. Domínguez Benavides %A G. López Acedo %A Hong Xu %T Weak uniform normal structure and iterative fixed points of nonexpansive mappings %J Colloquium Mathematicum %D 1995 %P 17-23 %V 68 %N 1 %U http://geodesic.mathdoc.fr/articles/10.4064/cm-68-1-17-23/ %R 10.4064/cm-68-1-17-23 %G en %F 10_4064_cm_68_1_17_23
T. Domínguez Benavides; G. López Acedo; Hong Xu. Weak uniform normal structure and iterative fixed points of nonexpansive mappings. Colloquium Mathematicum, Tome 68 (1995) no. 1, pp. 17-23. doi: 10.4064/cm-68-1-17-23
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