Abstract
Suppose
K
is a closed convex subset of a strictly convex real Banach space
E
which has a uniformly Gâteaux differentiable norm. Suppose that every nonempty closed convex bounded subset of
E
has the fixed point property for nonexpansive mappings. A strong convergence theorem is proved for a common zero of a family of
m
-accretive mappings from
K
to
E
. As a consequence, an iterative method is constructed to converge to a common fixed point (assuming existence) of a family of pseudocontractive mappings from
K
to
E
under certain mild condition.