  It is shown that if a Banach space X has the weak Banach-Saks property and
the weak fixed point property for nonexpansive mappings and Y satisfies
property asymptotic (P) (which is weaker than the condition WCS(Y)>1), then the
direct sum of X and Y endowed with a strictly monotone norm enjoys the weak
fixed point property. The same conclusion is valid if X admits a
1-unconditional basis.
