# Strong convergence of Krasnoselski-Mann iteration for a countable family of asymptotically nonexpansive mappings in CAT(0) spaces

Volume 10, Issue 4, pp 1326--1333 Publication Date: April 20, 2017       Article History
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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.

### Keywords

• Krasnoselski-Mann iteration
• CAT(0) spaces
• infinite families of nonexpansive mappings
• strong convergence
• $\Delta$-convergence.

•  47H09
•  47H10
•  47J25

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