VISCOSITY APPROXIMATION METHODS OF AVERAGING ITERATION FOR NONEXPANSIVE NONSELF-MAPPINGS

Lin-Fang Xing (P. R. China) and Rudong Chen (P. R. China)

Received February 17, 2007

Abstract

Let C be a nonempty closed convex subset of Hilbert space H, T be a nonexpansive nonself-mapping from C into H satisfying the weakly inward condition and and be a fixed contraction mapping. In this paper, we study the following sequences generated by where is a real sequence such that and P is the metric projection from H onto C. We prove that strongly converges to a fixed point of T as satisfying appropriate conditions. The results presented extend and improve the corresponding results of Matsushita and Kuroiwa [2] and Song and Chen [3].

Keywords and phrases: strong convergence, nonexpansive nonself-mapping, weakly inward condition.