A nonempty intersection theorem in general topological spaces and its applications 一般拓撲空間中的一個非空交定理及其應用
At first , we introduce a class of generalized s - r - kkm type mapping in g - convex space , and establish generalized s - r - kkm type nonempty intersection theorem under the noncompact setting of g - convex space . as for application , some new minimax inequalities , saddle point theorem and existence theorem of maximal elements are proved in g - convex spaces ; second , by using the generalized r - kkm mapping and generalized r - kkm theorems in [ 13 ] , some new existence theorem of maximal elements , existence theorem of equilibrium point for the abstract generalized vector equilibrium problem and existence theorem of solutions for equilibrium problem with lower and upper bounds are obtained in topological spaces 首先,我們在g -凸空間內(nèi)引入了廣義s - r - kkm型映像,并在非緊設置下建立了一類新的廣義s - r - kkm型非空交定理,作為應用,證明了g -凸空間內(nèi)一些新的極大極小不等式、鞍點定理和極大元存在定理;其次,利用文[ 13 ]中引入的廣義r - kkm映像和廣義r - kkm定理,在拓撲空間上得到了一些新的極大元存在定理、抽象廣義矢量平衡問題平衡點的存在定理和有上下界的平衡問題解的存在性定理。