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Equilibrium problems include variational inequalities , fixed point problem , complementarity problem , optimization, saddle point problem and the Nash equilibrium problem as special cases . Equilibrium problem for us to study from the financial , economic , optimal control and engineering technology and other fields generated a series of questions provides a systematic research framework , has attracted wide attention in recent years, the issue is a comprehensive and in-depth research in equilibrium problems , there is a very significant issue - the lower bound to bring balance, it was in 1999 by Isac, Sehgal and Singh proposed an open problem . bring lower bound for such balance, the existence of the solution , and the solution set of the stability of the algorithm is still the focus of the study . equilibrium problem for existence , algorithms and stability of solution sets , there are many research results, inspired by these results , this paper focuses on the lower bound to bring equilibrium problem , the main work is as follows : In the second chapter , the use of several classic not fixed point theorem has been put on the lower bound equilibrium Problems existence theorem ; Chapter III , in Hausdorff topological vector space K and discussed when the collection functionals f parameter λ and μ , respectively, subject to disturbances to bring the lower bound set of equilibrium Problems stability , in addition, the vector metric spaces discussed when K fixed , f parameter ε perturbed by the lower bound equilibrium Problems set to bring stability ; in the fourth chapter , namely the use of third-order differential Viscosity approximation method and critical point France constructed to bring the lower bound equilibrium Problems algorithms, and their convergence analysis algorithms do .
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