集值极大单调映象拓扑度的稳定性  

On the Homotopy Invariance of Topological Degree for Multivalued Maximal Monotone Mappings

作　　者：王伟[1] 蒋平川[1] 

机构地区：[1]广东工业大学应用数学学院,广东广州510520

出　　处：《广东工业大学学报》2014年第1期55-58,共4页Journal of Guangdong University of Technology

摘　　要：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.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 .

关 键 词：极大单调映象 拓扑度 同伦不变性 连续性 Yosida近似 

分 类 号：O177.91[理学—数学]