ABSTRACT
A Banach space X is said to have weakly fixed point property (WFPP) if any nonexpansive self-mapping on a non-empty weakly compact convex subset of X has a fixed point.
Let {*„} be a nonconstant sequence in X. If for any x e ca{xw}, the convex hull of }, the limit A(x) = lim,, ||jc — xn\\ exists and A(x) is affine on co{xn), then {xn} is
called a limit affine sequence. If in particular, A(x) is a constant on co{x„}, then {*„} is called a limit constant sequence. If X contains no weakly convergent limit affine sequence {*„} such that A(x„) is non-decreasing, then X is said to have weak sum-property ([6]). X is said to have weak normal structure (WNS) if it contains no weakly convergent limit constant sequence. It is known that
(weak sum-property) = > (WNS) = > (WFPP).
