集值极大单调映象拓扑度的稳定性

摘要

For a cluster of maximal monotone mappings , Hausdorff continuity of themselves and their do-main were constructed .The multi-valued mappings were transformed into single-valued mappings by means of their Yosida approximation , the homotopy invariance of Brouwer degree was used to approach its topological degree with the degree of its Yosida approximation , and the homotopy invariance of the degree for the cluster of maximal monotone mappings was obtained .Besides , some basic properties of the topolo-gical degree for the cluster of maximal monotone mappings as defined above were obtained .Similarly, un-der some additional assumptions , a theorem was derived about the homotopy invariance of the degree for the sum of two maximal monotone mappings .%对一簇极大单调映象，构造它们的定义域和映象本身的Hausdorff连续。用它的Yosida近似，将集值的情况转化为单值，用它的Yosida近似的拓扑度来逼近它的拓扑度。由连续函数Brouwer度的同伦不变性，得到这簇极大单调映象拓扑度的同伦不变性，并得到了这样定义的拓扑度的一些基本性质。类似地，在一些附加假设下，得到了两个极大单调映象和的拓扑度的同伦不变性的一个定理。