Title

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

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