Volume 32 • Number 2 • 2009   • 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 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]. 2000 Mathematics Subject Classification: 47H09, 47H10, 49J40, 47J20. Full text: PDF