intersection theorems meaning in English

相交定理

A nonempty intersection theorem in general topological spaces and its applications
一般拓扑空间中的一个非空交定理及其应用
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，我们在g -凸空间内引入了广义s - r - kkm型映像，并在非紧设置下建立了一类新的广义s - r - kkm型非空交定理，作为应用，证明了g -凸空间内一些新的极大极小不等式、鞍点定理和极大元存在定理；其次，利用文[ 13 ]中引入的广义r - kkm映像和广义r - kkm定理，在拓扑空间上得到了一些新的极大元存在定理、抽象广义矢量平衡问题平衡点的存在定理和有上下界的平衡问题解的存在性定理。