Weak convergence theorem by an extragradient method for variational inequality, equilibrium and fixed point problems
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Author list: Jaiboon C., Kumam P., Humphries U.W.
Publisher: Springer
Publication year: 2009
Journal: Bulletin of the Malaysian Mathematical Sciences Society (0126-6705)
Volume number: 32
Issue number: 2
Start page: 173
End page: 185
Number of pages: 13
ISSN: 0126-6705
eISSN: 2180-4206
Languages: English-Great Britain (EN-GB)
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Abstract
In this paper, we introduce a new iterative scheme for finding the common element of the set of: fixed points; equilibrium; and the variational inequality problems for monotone and k-Lipschitz continuous mappings. The iterative process is based on the so-called extragradient method. We show that the sequence converges weakly to a common element of the above three sets under some parameter controlling conditions. This main theorem extends a recent result of Nadezhkiha and Takahashi [7].
Keywords
k-Lipschitz continuous mapping
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