Strong convergence of an new iterative method for a zero of accretive operator and nonexpansive mapping
Meng Wen, Changsong Hu · Fixed Point Theory and Applications · 2012
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 algorithmwhere {a n } and {r n } are two sequences satisfying certain conditions, J r n denotes the resolvent (I + r n A) -1 for r n > 0, F be a strongly positive bounded linear operator on E is 0 < γ < γ , and j 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.