STRONG CONVERGENCE THEOREMS FOR ACCRETIVE OPERATORS AND NONEXPANSIVE MAPPINGS IN BANACH SPACES (Nonlinear Analysis and Convex Analysis)

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