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.
Qian, Shanguang 1 ; Deng, Wei-Qi 2
@article{10_22436_jnsa_010_04_04,
author = {Qian, Shanguang and Deng, Wei-Qi},
title = {Strong convergence of {Krasnoselski-Mann} iteration for a countable family of asymptotically nonexpansive mappings in {CAT(0)} spaces},
journal = {Journal of nonlinear sciences and its applications},
pages = {1326-1333},
year = {2017},
volume = {10},
number = {4},
doi = {10.22436/jnsa.010.04.04},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.22436/jnsa.010.04.04/}
}
TY - JOUR AU - Qian, Shanguang AU - Deng, Wei-Qi TI - Strong convergence of Krasnoselski-Mann iteration for a countable family of asymptotically nonexpansive mappings in CAT(0) spaces JO - Journal of nonlinear sciences and its applications PY - 2017 SP - 1326 EP - 1333 VL - 10 IS - 4 UR - http://geodesic.mathdoc.fr/articles/10.22436/jnsa.010.04.04/ DO - 10.22436/jnsa.010.04.04 LA - en ID - 10_22436_jnsa_010_04_04 ER -
%0 Journal Article %A Qian, Shanguang %A Deng, Wei-Qi %T Strong convergence of Krasnoselski-Mann iteration for a countable family of asymptotically nonexpansive mappings in CAT(0) spaces %J Journal of nonlinear sciences and its applications %D 2017 %P 1326-1333 %V 10 %N 4 %U http://geodesic.mathdoc.fr/articles/10.22436/jnsa.010.04.04/ %R 10.22436/jnsa.010.04.04 %G en %F 10_22436_jnsa_010_04_04
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 its applications, Tome 10 (2017) no. 4, p. 1326-1333. doi: 10.22436/jnsa.010.04.04
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