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Vietnam Journal of Mathematics 40:2&3(2012)
319-330
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An Iteration Method for Finding the Unique
Solution of a
Variational Inequality Problem Constrained by the
Intersection of the Sets
of Fixed Points of a Countable Family of
Nonexpansive Mappings
in Hilbert Spaces
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Lai-Jiu Lin and Chih-Sheng Chuang
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Department of Mathematics, National Changhua
University of Education,
Changhua,
50058, Taiwan
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Dedicated to Professor
Phan Quoc Khanh on the occasion of his 65th birthday
Received October 14,
2011
Revised January 18,
2012
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Abstract. In this paper, we consider an iteration
process which converges strongly to a common fixed point of a countable
family of nonexpansive mappings, and it is the unique solution of a
variational inequality constrained by this set of common fixed points. Note
that our results generalize the corresponding results by Ceng et al.
(Comput. Math. Appl. 61 (2011), 2447-2455).
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2000 Mathematics
Subject Classification. 47H10, 47H05, 47H17.
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Keywords. Variational
inequality, common fixed point, nonexpansive mapping.
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Established
by Vietnam Academy of Science and Technology &
Vietnam Mathematical Society
Published by
Springer since January 2013
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