Strong convergence of an new iterative method for a zero of accretive operator and nonexpansive mapping

Let E be a Banach space and A an m-accretive operator with a zero. Consider the iterative method that generates the sequence {x (n) } by the algorithm , where {a (n) } and {r (n) } are two sequences satisfying certain conditions, denotes the resolvent (I + r (n) A)(-1) for r (n) > 0, F be a strongly positive bounded linear operator on E is , and I center dot be a MKC on E. Strong convergence of the algorithm {x (n) } is proved assuming E either has a weakly continuous duality map or is uniformly smooth. MSC: 47H09; 47H10.