中文摘要：

上下界平衡问题是向量平衡问题中的一个很有意义的问题,它是G.Isac,V.M.Sechgal,S.P.Singh（Indian J Math,1999,41（1）：25-31.）公开提出的,并逐渐成为非线性分析中重要且有效的工具.建立了关于FC-凸包的新的非空交定理,通过应用这个非空交定理和不动点定理,解决了上下界平衡问题和拟平衡问题解的存在问题,这些结论在更弱的假设条件下回答了以上所提到的公开问题.从而改进了最近文献中的相关结果.

英文摘要：

Equilibrium problem with lower and upper bounds is a very interesting problem of equilibrium problem,which was introduced by G.Isac,V.M.Sechgal,S.P.Singh（Indian J Math,1999,41（1） ： 25-31.） and then become a very important and valued tool in nonlinear analysis.Firstly,we obtain a new nonempty intersection theorem about FC-hull.By using this nonempty intersection theorem and fixed point theorem,some new theorems of equilibrium problems and quasi-equilibrium problems with lower and upper bounds are established in noncompact FC-spaces.The results presented in this paper answer the above open problem and generalize some known results in the literature.