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

• Main Authors: Laowang W., Panyanak B.
• Format: Article
• Published: Springer Publishing Company 2015
• Subjects: Geometry and Topology; Applied Mathematics
• Online Access: http://www.scopus.com/inward/record.url?partnerID=HzOxMe3b&scp=78649448016&origin=inward; http://cmuir.cmu.ac.th/handle/6653943832/38588
• Institution: Chiang Mai University

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 ⊕ β nTxn]), 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. Copyright © 2010 W. Laowang and B. Panyanak.