Published online by Cambridge University Press: 05 May 2009
In this paper, we introduce an iterative scheme using an extragradient method for finding a common element of the set of solutions of a generalized equilibrium problem, the set of fixed points of a nonexpansive mapping and the set of the variational inequality for a monotone, Lipschitz-continuous mapping. We obtain a weak convergence theorem for three sequences generated by this process. Based on this result, we also obtain several interesting results. The results in this paper generalize and extend some well-known weak convergence theorems in the literature.
The first author was supported by the National Natural Science Foundation of China (grant number 10771228), the Science and Technology Research Project of Chinese Ministry of Education (grant number 206123), the Education Committee project Research Foundation of Chongqing (grant number KJ070816). The second author was partially supported by the grant NSC96-2628-E-110-014-MY3.