Strong convergence of averaging iterations of nonexpansive nonself-mappings

Let C be a closed convex subset of Hilbert space H, T a nonexpansive nonself-mapping from C into H, and x0,x,y0,y elements of C. In this paper, we study the convergence of the two sequences generated by xn+1 = 1 n+ 1 n j=0 αnx + (1 − αn)(P T )j xn for n = 0, 1, 2, . . . , yn+1 = 1 n+ 1 n j=0 P αny + (1 − αn)(T P)j yn for n = 0, 1, 2, . . . , where {αn} is a real sequence such that 0 αn 1, and P is the metric projection from H onto C.  2004 Elsevier Inc. All rights reserved