There is an equivalent norm on ℓ1 that has the fixed point property
Abstract
Let γk = frac(8k, 1 + 8k) for all k ∈ N, and let {triple vertical-rule fence} {dot operator} {triple vertical-rule fence} be the equivalent norm of ℓ1 defined by {triple vertical-rule fence} (an) {triple vertical-rule fence} = under(sup, k ∈ N) γk underover(∑, n = k, ∞) | an | for all x = (an) ∈ ℓ1 . We prove that (ℓ1, {triple vertical-rule fence} {dot operator} {triple vertical-rule fence}) has the fixed point property for nonexpansive self-mappings. © 2007 Elsevier Ltd. All rights reserved.
Publication Title
Nonlinear Analysis, Theory, Methods and Applications
Recommended Citation
Lin, P. (2008). There is an equivalent norm on ℓ1 that has the fixed point property. Nonlinear Analysis, Theory, Methods and Applications, 68 (8), 2303-2308. https://doi.org/10.1016/j.na.2007.01.050
