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Volume 27, Issue 4
Approximation of the Nearest Common Fixed Point of Asymptotically Nonexpansive Mappings in Banach Spaces

Xiongrui Wang

Commun. Math. Res., 27 (2011), pp. 369-377.

Published online: 2021-05

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  • Abstract

In this paper, the iteration $x_{n+1} = α_ny + (1 − α_n)T^{k(n)}_{i(n)} x_n$ for a family of asymptotically nonexpansive mappings $T_1, T_2, · · · , T_N$ is originally introduced in a uniformly convex Banach space. Motivated by recent papers, we prove that under suitable conditions the iteration scheme converges strongly to the nearest common fixed point of the family of asymptotically nonexpansive mappings. The results presented in this paper expand and improve corresponding ones from Hilbert spaces to uniformly convex Banach spaces, or from nonexpansive mappings to asymptotically nonexpansive mappings.

  • Keywords

asymptotically nonexpansive mapping, sunny nonexpansive retraction, uniformly Gâteaux differentiable, weakly sequentially continuous duality.

  • AMS Subject Headings

47H09

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CMR-27-369, author = {Xiongrui and Wang and and 18428 and and Xiongrui Wang}, title = {Approximation of the Nearest Common Fixed Point of Asymptotically Nonexpansive Mappings in Banach Spaces}, journal = {Communications in Mathematical Research }, year = {2021}, volume = {27}, number = {4}, pages = {369--377}, abstract = {

In this paper, the iteration $x_{n+1} = α_ny + (1 − α_n)T^{k(n)}_{i(n)} x_n$ for a family of asymptotically nonexpansive mappings $T_1, T_2, · · · , T_N$ is originally introduced in a uniformly convex Banach space. Motivated by recent papers, we prove that under suitable conditions the iteration scheme converges strongly to the nearest common fixed point of the family of asymptotically nonexpansive mappings. The results presented in this paper expand and improve corresponding ones from Hilbert spaces to uniformly convex Banach spaces, or from nonexpansive mappings to asymptotically nonexpansive mappings.

}, issn = {2707-8523}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/cmr/19080.html} }
TY - JOUR T1 - Approximation of the Nearest Common Fixed Point of Asymptotically Nonexpansive Mappings in Banach Spaces AU - Wang , Xiongrui JO - Communications in Mathematical Research VL - 4 SP - 369 EP - 377 PY - 2021 DA - 2021/05 SN - 27 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/cmr/19080.html KW - asymptotically nonexpansive mapping, sunny nonexpansive retraction, uniformly Gâteaux differentiable, weakly sequentially continuous duality. AB -

In this paper, the iteration $x_{n+1} = α_ny + (1 − α_n)T^{k(n)}_{i(n)} x_n$ for a family of asymptotically nonexpansive mappings $T_1, T_2, · · · , T_N$ is originally introduced in a uniformly convex Banach space. Motivated by recent papers, we prove that under suitable conditions the iteration scheme converges strongly to the nearest common fixed point of the family of asymptotically nonexpansive mappings. The results presented in this paper expand and improve corresponding ones from Hilbert spaces to uniformly convex Banach spaces, or from nonexpansive mappings to asymptotically nonexpansive mappings.

Xiongrui Wang. (2021). Approximation of the Nearest Common Fixed Point of Asymptotically Nonexpansive Mappings in Banach Spaces. Communications in Mathematical Research . 27 (4). 369-377. doi:
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