Mixed Equilibrium Problems And Balance Problems Of Multi-valued Auxiliary Iterative Algorithm

In this paper, we study a class of generalized nonlinear mixed equilibrium problems which are new, also study mixed general equilibrium problems and multivalued equilibrium problems.In the second chapter, we use the auxiliary principle technique to study a class of generalized nonlinear mixed equilibrium problems which are new. We prove the existence of the solution of the auxiliary problem for the generalized nonlinear mixed equilibrium problems and show the existence of the solution by using the auxiliary principle technique. We also prove the convergence of iterative sequences generated by the algorithm.In the third chapter, we introduce the auxiliary principle technique to study a class of mixed general equilibrium problems.We prove the existence of the solution of the auxiliary problem for the mixed general equilibrium problems and show the existence of the solution by using the auxiliary principle technique. We also prove the convergence of iterative sequences generated by the algorithm.In the forth chapter, we use the auxiliary principle technique to study a multivalued equilibrium problems,we also prove that the convergence of the suggested methods requires only the partially relaxed strongly monotonicity and pseudomonotonicity.In all, the result presented in the papper generalized and unify known results in rescents liternatures.