Variational-Like Inequalities And Equilibrium Problems

This paper mainly further studies several focus problems in nonlinear functional analysis unifies and generalizes some known results in recent literature.At first , a new extragradient iterative algorithm for solving the variational inequality problem on Rn is suggested. By using Mann iterative scheme, new searching direction and better step-size rule, the algorithm is different from any one in existing projection-type methods. Under a certain generalized monotonity condition, the global convergence of the iterative sequence generated by the new algorithm is proved.Next, we introduce some new systems of abstract generalized vector quasi-equilibrium problem in G-convex space. By applying the fixed point theorem of set-valued mappings of nocompact product G-convex space, some new existence theorems of system of generalized vector quasi-equibrium problems are proved, and this results extend the applictions of the fixed point theorem.