Geodesic
Weak Convergence Theorem by an Extragradient Method for Variational Inequality, Equilibrium and Fixed Point Problems
Bulletin of the Malaysian Mathematical Society, Tome 32 (2009) no. 2 Cet article a éte moissonné depuis la source Bulletin of the Malaysian Mathematical Society website

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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].
Classification : 47H09, 47H10, 49J40, 47J20. 
@article{BMMS_2009_32_2_a6,
     author = {C. Jaiboon and P. Kumam and U. W. Humphries},
     title = {Weak {Convergence} {Theorem} by an {Extragradient} {Method} for {Variational} {Inequality,} {Equilibrium} and {Fixed} {Point} {Problems}},
     journal = {Bulletin of the Malaysian Mathematical Society},
     year = {2009},
     volume = {32},
     number = {2},
     url = {http://geodesic.mathdoc.fr/item/BMMS_2009_32_2_a6/}
}
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C. Jaiboon; P. Kumam; U. W. Humphries. Weak Convergence Theorem by an Extragradient Method for Variational Inequality, Equilibrium and Fixed Point Problems. Bulletin of the Malaysian Mathematical Society, Tome 32 (2009) no. 2. http://geodesic.mathdoc.fr/item/BMMS_2009_32_2_a6/