Strong convergence of averaging iterations of nonexpansive nonself-mappings

By S. Matsushita, Daishi Kuroiwa. 2004

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Abstract 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 x n+1 = 1 n+1 ∑ j=0 n α n x+(1−α n )(PT) j x n for n=0,1,2,…, y n+1 = 1 n+1 ∑ j=0 n P α n y+(1−α n )(TP) j y n 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.

Subfields: Computational Theory and Mathematics, Geometry and Topology, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/0361c68598955d24e7a3a1f6472470fb304faf48