Abstract
The main purpose of this paper is to study an iteration procedure for finding
a common fixed point of a countable family of nonexpansive mappings in Banach
spaces. We introduce a Mann type iteration procedure. Then we prove that such a sequence
converges weakly to a common fixed point of a countable family of nonexpansive
mappings. Moreover, we apply our result to the problem of finding a common fixed
point of a pair of nonexpansive mappings and the problem of finding a common solution
of the fixed point problem and the variational inequality problem.
