Strong convergence of averaging iterations of nonexpansive nonself-mappings

AbstractLet 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=1n+1∑j=0nαnx+(1−αn)(PT)jxnforn=0,1,2,…,yn+1=1n+1∑j=0nPαny+(1−αn)(TP)jynforn=0,1,2,…, where {αn} is a real sequence such that 0⩽αn⩽1, and P is the metric projection from H onto C