A relaxed extragradient approximation method of two inverse-strongly monotone mappings for a general system of variational inequalities, fixed point and equilibrium problems
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Publication Details
Author list: Kumam P.
Publisher: Springer
Publication year: 2010
Journal: Bulletin of the Iranian Mathematical Society (1017-060X)
Volume number: 36
Issue number: 1
Start page: 227
End page: 250
Number of pages: 24
ISSN: 1017-060X
eISSN: 1735-8515
Languages: English-Great Britain (EN-GB)
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Abstract
We introduce and study an iterative sequence for finding the common element of the set of fixed points of a nonexpansive mapping, the set of solutions of an equilibrium problem and the solutions of the general system of variational inequality for two inverse-strongly monotone mappings. Under suitable conditions, some strong convergence theorems for approximating a common element of the above three sets are obtained. Moreover, using the above theorem, we also find solutions of a general system of variational inequalities and a zero of a maximal monotone operator in a real Hilbert space. As applications, we utilize our results to study the zeros of the maximal monotone and some convergence problem for strictly pseudocontractive mappings. Our results include the previous results as special cases extending and improving the results of Ceng et al. [4], Yao and Yao [18] and some others. ฉ 2010 Iranian Mathematical Society.
Keywords
Equilibrium problems, Relaxed extragradient
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