




Volume 32 • Number 2 • 2009 

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Weak Convergence Theorem by an Extragradient Method for Variational Inequality, Equilibrium and Fixed Point Problems
C. Jaiboon, P. Kumam and U. W. Humphries
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 kLipschitz continuous mappings. The
iterative process is based on the socalled 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].
2000 Mathematics Subject Classification: 47H09, 47H10, 49J40, 47J20.
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