The Locally Uniform Nonsquare in Generalized Cesàro Sequence Spaces

Abstract

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.