A new iterative algorithm on nonlinear mappings in Banach spaces

We first introduce a new iterative algorithm generated by two relatively nonexpansive mappings and a monotone operator in a 2-uniformly convex and uniformly smooth Banach space. Then we prove that this algorithm converges strongly to a common element of the set of the fixed points of two relatively nonexpansive mappings and the set of zero points of the monotone operator. Finally, we apply our convergence theorem to the problem of finding a minimizer of a convex function and a zero point of a monotone operator.