Approximating Fixed Points of Nonexpansive Nonself Mappings in CAT(0) Spaces. (2nd December 2009)

• Record Type: Journal Article
• Authors: Laowang, W.; Panyanak, B.
• Other Names: Suzuki Tomonari Academic Editor.
• Is Part Of: Fixed point theory and applications. Volume 2010(2010)
• Publication Date: 2009-12-02
• Subjects: Fixed point theory -- Periodicals; Mappings (Mathematics) -- Periodicals; 515.7248
• DOI: 10.1155/2010/367274
• Languages: English
• ISSNs: 1687-1812

Abstract

Abstract : Suppose thatK is a nonempty closed convex subset of a complete CAT(0) spaceX with the nearest point projectionP fromX ontoK . LetT : K → X be a nonexpansive nonself mapping withF ( T ) : = { x ∈ K : T x = x } ≠ ∅ . Suppose that{ x n } is generated iteratively byx 1 ∈ K, x n + 1 = P ( ( 1 − α n ) x n ⊕ α n T P [ ( 1 − β n ) x n ⊕ β n T x n ] ), n ≥ 1, where{ α n } and{ β n } are real sequences in[ ε, 1 − ε ] for someε ∈ ( 0, 1 ) . Then{ x n } Δ -converges to some pointx ∗ inF ( 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.