We prove the following: Let $C$ be a nonempty weakly compact convex subset of a strictly convex Banach space, and $T:C\to C$ be a nonexpansive mapping . Then $F(T)= \bigcap\limits_{\epsilon >0} \overline{F_\epsilon{(T)}}^\omega $ if and only if $F(T) = \bigcap\limits_{\epsilon>0} \overline{co}F_\epsilon (T)$, where $F(T)$ and $F_\epsilon(T)$ are the fixed point and $\epsilon$-approximate fixed point sets of $T$, respectively.
