There is an equivalent norm on ℓ1ℓ1 that has the fixed point property

Let γk=8k1+8k for all k∈Nk∈N, and let ⦀⋅⦀⦀⋅⦀ be the equivalent norm of ℓ1ℓ1 defined by ⦀(an)⦀=supk∈Nγk∑n=k∞|an|for all x=(an)∈ℓ1. We prove that (ℓ1,⦀⋅⦀)(ℓ1,⦀⋅⦀) has the fixed point property for nonexpansive self-mappings.