The Relationship Between Solution Of Equilibrium Problems In Different Spaces

In recent years,the split feasibility problem with a strong application back-ground is a hot topic in the nonlinear functional analysis.The idea of split feasi-bility issue has produced split equilibrium problems for the study of equilibrium problems in different spaces.This thesis proposes a new algorithm is used to study the relation of solutions to the equilibrium problem on different Hilbert space,in this thesis:First of all,in the Hilbert space,we consider the common elements of the solution of the split equality equilibrium problem and the fixed point of asymp-totically nonexpansive mapping.Under the constraint of no demi-compact,we obtain the strong convergence theorem of the common element of the solution of the split equality equilibrium problem and asymptotically nonexpansive mapping.Next,in the Hilbert space,we consider the common elements of the solution of the split equality mixed equilibrium problem and the fixed point of asymptoti-cally nonexpansive mapping.Under the constraint of no demi-compact,we obtain the strong convergence theorem of the common element of the solution of the split equality mixed equilibrium problem and asymptotically nonexpansive mapping.Finally,the results obtained in this thesis are used to study the problem of mixed variational inequalities and the convex minimization of the split equality,and the results in the existing literature are improved and generalized.