Strong convergence of Krasnoselski-Mann iteration for a countable family of asymptotically nonexpansive mappings in CAT(0) spaces
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Authors
Shanguang Qian
- Architectural Engineering Faculty, Kunming Metallurgy College, Kunming, Yunnan, P. R. China.
Wei-Qi Deng
- School of Statistics and Mathematics, Yunnan University of Finance and Economics, Kunming, Yunnan, P. R. China.
Abstract
Based on a specific way of choosing the indices and a new concept, namely, an analogue of inner product, a modified
Krasnoselski-Mann iteration scheme is proposed for approximating common fixed points of a countable family of asymptotically
nonexpansive mappings; and a strong convergence theorem is established in the framework of CAT(0) spaces. Our results greatly
improve and extend those of the authors whose related researches just involve a single mapping and the weaker \(\Delta\)-convergence.
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ISRP Style
Shanguang Qian, Wei-Qi Deng, Strong convergence of Krasnoselski-Mann iteration for a countable family of asymptotically nonexpansive mappings in CAT(0) spaces, Journal of Nonlinear Sciences and Applications, 10 (2017), no. 4, 1326--1333
AMA Style
Qian Shanguang, Deng Wei-Qi, Strong convergence of Krasnoselski-Mann iteration for a countable family of asymptotically nonexpansive mappings in CAT(0) spaces. J. Nonlinear Sci. Appl. (2017); 10(4):1326--1333
Chicago/Turabian Style
Qian, Shanguang, Deng, Wei-Qi. "Strong convergence of Krasnoselski-Mann iteration for a countable family of asymptotically nonexpansive mappings in CAT(0) spaces." Journal of Nonlinear Sciences and Applications, 10, no. 4 (2017): 1326--1333
Keywords
- Krasnoselski-Mann iteration
- CAT(0) spaces
- infinite families of nonexpansive mappings
- strong convergence
- \(\Delta\)-convergence.
MSC
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