STRONG CONVERGENCE THEOREMS FOR ACCRETIVE OPERATORS AND NONEXPANSIVE MAPPINGS IN BANACH SPACES (Nonlinear Analysis and Convex Analysis)
Jong Soo Jung · Kyoto University Research Information Repository (Kyoto University) · 2018
In this paper, we introduce two new iterative algorithms (one implicit and one explicit) for finding a common point of the set of zeros of an accretive operator and the set of fixed points of a nonexpansive mapping in a real uniformly convex Banach space having a uniformly Gâteaux differentiable norm. Then under suitable control conditions, we establish strong convergence of sequence generated by proposed algorithm to a common point of above two sets, which is a solution of a ceratin variational inequality. The main theorems develop and complement some well-known results in the literature.