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Approximation of common fixed points of an infinite family of nonexpansive mappings in Banach spaces

โœ Scribed by Yeol Je Cho; Shin Min Kang; Xiaolong Qin

Publisher
Elsevier Science
Year
2008
Tongue
English
Weight
261 KB
Volume
56
Category
Article
ISSN
0898-1221

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โœฆ Synopsis

Let C be a closed convex subset of a real uniformly smooth and strictly convex Banach space E. Consider the following iterative algorithm given by

where f is a contraction on C and W n is a mapping generated by an infinite family of nonexpansive mappings {T i } โˆž i=1 . Assume that the set of common fixed points of this infinite family of nonexpansive mappings is not empty.

In this paper, we prove that the sequence {x n } generated by the above iterative algorithm converges strongly to a common fixed point of {T i } โˆž i=1 , which solves some variational inequality. Our results improve and extend the results announced by many others.

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