The purpose of this paper is to get strong convergence theorems for a countable family of
relatively quasi-nonexpansive mappings fSng
1
n¼0, a maximal monotone operator T, and a generalized mixed equilibrium problem in a uniformly smooth and uniformly convex Banach space lacking
condition UARC. Two examples are given to support our results. One is a countable family of
uniformly closed relatively quasi-nonexpansive mappings but not a countable family of relatively
nonexpansive mappings. Another is uniformly closed but not satisfies condition UARC. Many
recent results in this field have been unified and improved.