Abstract and Applied Analysis

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

Luo Yi Shi, Ru Dong Chen, and Yu Jing Wu

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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 C is arbitrary and x n + 1 = α n x n ( 1 - α n ) T n y n or x 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 for n 1 , where { α n } , { β n } ( 0,1 ) . It is shown that under certain appropriate conditions on α n , β 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

Permanent link to this document
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


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