Journal of Inequalities and Applications
Volume 2008 (2008), Article ID 162037, 10 pages
The Locally Uniform Nonsquare in Generalized Cesàro Sequence Spaces
Department of Mathematics, Faculty of Science, Naresuan University, Phitsanulok 65000, Thailand
Received 20 August 2008; Accepted 10 November 2008
Academic Editor: Martin J. Bohner
Copyright © 2008 Narin Petrot. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
We show that the generalized Cesàro sequence spaces possess the locally
uniform nonsquare and have the fixed point property, but they are not uniformly
nonsquare. This result is related to the result of the paper by J. Falset et
al. (2006) by giving the examples and the motivation to find the geometric
properties that are weaker than uniformly nonsquare but still possess the
fixed point property in any Banach spaces.