Journal
COMPUTERS & MATHEMATICS WITH APPLICATIONS
Volume 56, Issue 8, Pages 2058-2064Publisher
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.camwa.2008.03.035
Keywords
Nonexpansive mapping; Contraction; Strong convergence; Fixed point
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Funding
- Korean Government (MOEHRD) [KRF2007-313-C00040]
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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 [GRAPHICS] where f is a contraction on C and W. is a mapping generated by an infinite family of nonexpansive mappings {Ti}(i=1)(infinity). 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 {Ti}(i=1)(infinity), which solves some variational inequality. Our results improve and extend the results announced by many others. (c) 2008 Elsevier Ltd. All rights reserved.
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