无凸假定条件的不动点定理及其应用(英文)

Some Fixed Point Theorems Without Convexity Assumptions and Applications

在本文中,在不具有凸假定的情形下,扩展集值Browder形式的不动点定理.进一步,在局部凸拓扑向量空间,相应的Fan-Glicksberg情形的不动点定理被推导.作为应用,在无凸假定的条件下,我们得到相关的连续选择定理,Ky Fan极小极大不等式和非合作博弈Nash均衡的存在性结论.

In this paper,the generalized Browder-type fixed point theorem on Hausdorff topological vector space is introduced, which can be regarded as a generalization of the Browder-type fixed point theorem for the set-valued mapping without convexity assumption. Further,on locally convex topol- ogical vector space,Fan-Glicksberg-type fixed point theorem is studied. As the applications,section theorem,Ky Fan minimax inequality and existence theorem of Nash equilibrium for non-cooperative games without convexity assumption are established.