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We show that every subset of L 1 (0,1) that contains the nontrivial inter- section of an order interval and finitely many hyperplanes fails to have the fixed point property for nonexpansive mappings.

New fixed point free nonexpansive maps on weakly compact, convex subsets of L1[0,1]

New fixed point free nonexpansive maps on weakly compact, convex subsets of L¹[0,1]