集值映象的图象拓扑与不动点的通有稳定性

THE GRAPH TOPOLOGY OF SET-VALUED MAPPINGS AND THE GENERIC STABILITY OF FIXED POINTS

本文进一步研究了上半连续集值映象不动点的稳定性问题，在集值映象的图象拓扑的意义下，我们证明了不动点的通有稳定性，也就是说，在Ｂａｉｒｅ分类的意义下，绝大多数的映象具有本质不动点．

In this paper, we have given a further study for the stability of fixed points. We have proved that the sets of fixed points of set-valued mappings have generic stability with respect to the graph topology, i.e., in the sense of Baire category, for most mappings all their fixed points are essential.