Research Of Equilibrium Problem Based On Variational Inequality

The formulation of equilibrium problems is quite general and makes it a versatile tool for the investigation of various problems arising in pure and applied mathematics, physics, econom-ics and operation research. The research results can be generalized to the variational inequal-ities, the fixed point theory, theory of Nash equilibrium.For the operator iteration convergence problem of equilibrium problem.use the viscosity approximation methods,which introduce new iteration algorithm for finding a common element of the set of solutions of the general variational inequalities and the set of fixed points of a non-expansive mapping;the set of equilibrium problems and the set of fixed points of nonexpan-sive mapping, the results improve and extend the results of the related literature,the strong convergence is proved.Establish the numerical simulations for the equilibrium problem and the fixed points of non-expansive mappings, which select different values of parameters and the iteration has different results, finally find the optimal parameter values.