广东工业大学学报
廣東工業大學學報
엄동공업대학학보
JOURNAL OF GUANGDONG UNIVERSITY OF TECHNOLOGY
2014年
1期
55-58
,共4页
极大单调映象%拓扑度%同伦不变性%连续性%Yosida近似
極大單調映象%拓撲度%同倫不變性%連續性%Yosida近似
겁대단조영상%탁복도%동륜불변성%련속성%Yosida근사
maximal monotone mapping%topological degree%the homotopy invariance%continuity%Yosi-da approximation
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。
對一簇極大單調映象，構造它們的定義域和映象本身的Hausdorff連續。用它的Yosida近似，將集值的情況轉化為單值，用它的Yosida近似的拓撲度來逼近它的拓撲度。由連續函數Brouwer度的同倫不變性，得到這簇極大單調映象拓撲度的同倫不變性，併得到瞭這樣定義的拓撲度的一些基本性質。類似地，在一些附加假設下，得到瞭兩箇極大單調映象和的拓撲度的同倫不變性的一箇定理。
대일족겁대단조영상，구조타문적정의역화영상본신적Hausdorff련속。용타적Yosida근사，장집치적정황전화위단치，용타적Yosida근사적탁복도래핍근타적탁복도。유련속함수Brouwer도적동륜불변성，득도저족겁대단조영상탁복도적동륜불변성，병득도료저양정의적탁복도적일사기본성질。유사지，재일사부가가설하，득도료량개겁대단조영상화적탁복도적동륜불변성적일개정리。
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 .
