△-Convergence Problems for Asymptotically Nonexpansive Mappings in CAT(0) Spaces. (20th March 2013)

• Record Type: Journal Article
• Authors: Shi, Luo Yi; Chen, Ru Dong; Wu, Yu Jing
• Other Names: Song Yisheng Academic Editor.
• Is Part Of: Abstract and applied analysis. Volume 2013(2013)
• Publication Date: 2013-03-20
• Subjects: Mathematical analysis -- Periodicals; Mathematical analysis; Applied Mathematics; Mathematical Analysis; Periodicals; 515.05
• DOI: 10.1155/2013/251705
• Languages: English
• ISSNs: 1085-3375

Abstract

Abstract : New △-convergence theorems of iterative sequences for asymptotically nonexpansive mappings in CAT(0) spaces are obtained. Consider an asymptotically nonexpansive self-mappingT of a closed convex subsetC of a CAT(0) spaceX . Consider the iteration process{ x n }, wherex 0 ∈ C is arbitrary andx n + 1 = α n x n ⊕ ( 1 - α n ) T n y n orx n + 1 = α n T n x n ⊕ ( 1 - α n ) y n, y n = β n x n ⊕ ( 1 - β n ) T n x n forn ≥ 1, where{ α n }, { β n } ⊂ ( 0, 1 ) . It is shown that under certain appropriate conditions onα n, β n, { x n } △-converges to a fixed point ofT .