Viscosity approximation methods for monotone mappings and a countable family of nonexpansive mappings
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Author list: Kumam P., Plubtieng S.
Publication year: 2011
Volume number: 61
Issue number: 2
Start page: 257
End page: 274
Number of pages: 18
ISSN: 0139-9918
eISSN: 0139-9918
Languages: English-Great Britain (EN-GB)
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Abstract
We use viscosity approximation methods to obtain strong convergence to common fixed points of monotone mappings and a countable family of nonexpansive mappings. Let C be a nonempty closed convex subset of a Hilbert space H and PC is a metric projection. We consider the iteration process {xn} of C defined by x1 = x ∈ C is arbitrary and where f is a contraction on C, {Sn} is a sequence of nonexpansive self-mappings of a closed convex subset C of H, and A is an inverse-strongly-monotone mapping of C into H. It is shown that {xn} converges strongly to a common element of the set of common fixed points of a countable family of nonexpansive mappings and the set of solutions of the variational inequality for an inverse-strongly-monotone mapping which solves some variational inequality. Finally, the ideas of our results are applied to find a common element of the set of equilibrium problems and the set of solutions of the variational inequality problem, a zero of a maximal monotone operator and a strictly pseudocontractive mapping in a real Hilbert space. The results of this paper extend and improve the results of Chen, Zhang and Fan. © 2011 Versita Warsaw and Springer-Verlag Wien.
Keywords
accretive operator
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