Approximation of the Nearest Common Fixed Point of Asymptotically Nonexpansive Mappings in Banach Spaces
Year: 2011
Author: Xiongrui Wang
Communications in Mathematical Research , Vol. 27 (2011), Iss. 4 : pp. 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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2011-CMR-19080
Communications in Mathematical Research , Vol. 27 (2011), Iss. 4 : pp. 369–377
Published online: 2011-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 9
Keywords: asymptotically nonexpansive mapping sunny nonexpansive retraction uniformly Gâteaux differentiable weakly sequentially continuous duality.