Existence and iterative approximation methods for generalized mixed vector equilibrium problems with relaxed monotone mappings

We first consider an auxiliary problem for the generalized mixed vector equilibrium problem with a relaxed monotone mapping and prove the existence and uniqueness of the solution for the auxiliary problem. we then introduce a new iterative scheme for approximating a common element of the set of solutions of a generalized mixed vector equilibrium problem with a relaxed monotone mapping and the set of common fixed points of a countable family of nonexpansive mappings. the results presented in this paper can be considered as a generalization of some known results due to wang et al. (2010). © 2013 rabian wangkeeree and panu yimmuang.