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We study xed point theory for semi-strongly asymptotically nonexpansive and strongly asymptotically nonexpansive mappings. We consider these mappings for renormings of l 1 and c0, and show that l 1 cannot be equivalently renormed to have the xed point property for semi-strongly asymptotically nonexpansive mappings, while c0 cannot be equivalently renormed to have the xed point property for strongly asymptotically nonexpansive mappings. Next and more importantly, we show reexivity is equivalentdoi:10.15672/hjms.20174620775 fatcat:dgy6na7ctjc6bes62om36lkp4m