https://ogma.newcastle.edu.au/vital/access/ /manager/Index en-au 5 https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:34604 X,‖•‖) has the fixed point property (FPP); that is, every nonexpansive self-mapping defined on a closed, bounded, convex subset has a fixed point. In particular, P.K. Lin's norm in ℓ₁[14] and the norm v_p(•) (with p = (p_n) and lim_n p_n = 1) introduced in [3] are examples of near-infinity concentrated norms. When v_p(•) is equivalent to the ℓ₁-norm, it was an open problem as to whether (ℓ₁, v_p(•)) had the FPP. We prove that the norm v_p(•) always generates a nonreflexive Banach space X= ℝ ⊕_p₁ (ℝ ⊕_p₂ (ℝ ⊕_p₃...)) satisfying the FPP, regardless of whether v_p(•) is equivalent to the ℓ₁-norm. We also obtain some stability results.]]> Tue 23 Jun 2020 12:15:42 AEST ]]> https://ogma.newcastle.edu.au/vital/access/ /manager/Repository/uon:17735 Sat 24 Mar 2018 07:57:40 AEDT ]]>