Copyright © 2010 W. Laowang and B. Panyanak. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Suppose that K is a nonempty closed convex subset of a complete CAT(0) space X with the nearest point projection P from X onto K. Let T:K→X be a nonexpansive nonself mapping with F(T):={x∈K:Tx=x}≠∅. Suppose that {xn} is generated iteratively by x1∈K, xn+1=P((1−αn)xn⊕αnTP[(1−βn)xn⊕βnTxn]), n≥1, where {αn} and {βn} are real sequences in [ε,1−ε] for some ε∈(0,1). Then {xn}Δ-converges to some point x∗ in F(T). This is an analog of a result in Banach spaces of Shahzad (2005) and extends a result of Dhompongsa and Panyanak (2008) to the case of nonself mappings.