WEAK AND STRONG CONVERGENCE OF THE MODIFIED MANN ITERATION PROCESS FOR NONEXPANSIVE MAPPINGS

In this paper, we first show the weak convergence of the Moudafi iteration process of quasi-nonexpansive mapping and nonexpansive mapping in a real uniformly convex Banach space satisfying Opial's condition, which generalizes the result due to Reich [8]. Next, we show the weak convergence of the Modified Mann iteration process of nonexpansive mapping in a real uniformly convex Banach space such that its dual has the Kadec-Klee property, which generalizes the result due to Reich [8]. Finally, we show the strong convergence of the Modified Mann iteration process of nonexpansive mapping satisfying condition A, which generalizes the result due to Senter-Dotson [11].