Abstract and Applied Analysis

$/bigtriangleup$-Convergence Problems for Asymptotically Nonexpansive Mappings in CAT(0) Spaces

Abstract

New △-convergence theorems of iterative sequences for asymptotically nonexpansive mappings in CAT(0) spaces are obtained. Consider an asymptotically nonexpansive self-mapping $T$ of a closed convex subset $C$ of a CAT(0) space $X$. Consider the iteration process $\{{x}_{n}\}$, where ${x}_{0}\in C$ is arbitrary and ${x}_{n+1}={\alpha }_{n}{x}_{n}\oplus (1-{\alpha }_{n}){T}^{n}{y}_{n}$ or ${x}_{n+1}={\alpha }_{n}{T}^{n}{x}_{n}\oplus (1-{\alpha }_{n}){y}_{n},{y}_{n}={\beta }_{n}{x}_{n}\oplus (1-{\beta }_{n}){T}^{n}{x}_{n}$ for $n\ge 1$, where $\{{\alpha }_{n}\},\{{\beta }_{n}\}\subset (0,1)$. It is shown that under certain appropriate conditions on ${\alpha }_{n},{\beta }_{n},\{{x}_{n}\}$  △-converges to a fixed point of $T$.

Article information

Source
Abstr. Appl. Anal., Volume 2013, Special Issue (2013), Article ID 251705, 6 pages.

Dates
First available in Project Euclid: 26 February 2014

https://projecteuclid.org/euclid.aaa/1393444404

Digital Object Identifier
doi:10.1155/2013/251705

Mathematical Reviews number (MathSciNet)
MR3035361

Zentralblatt MATH identifier
1273.47114

Citation

Shi, Luo Yi; Chen, Ru Dong; Wu, Yu Jing. $/bigtriangleup$ -Convergence Problems for Asymptotically Nonexpansive Mappings in CAT(0) Spaces. Abstr. Appl. Anal. 2013, Special Issue (2013), Article ID 251705, 6 pages. doi:10.1155/2013/251705. https://projecteuclid.org/euclid.aaa/1393444404