Fixed Point Theory and Applications
Volume 2010 (2010), Article ID 367274, 11 pages
doi:10.1155/2010/367274

Approximating fixed points of nonexpansive nonself mappings in CAT(0) spaces

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.