关于保序集值算子的讨论  

On Order Preserving Set-valued Operator

作　　者：王名燕[1] 郭春梅[1] 

机构地区：[1]山西大学数学科学学院,山西太原030006

出　　处：《山西大学学报（自然科学版）》2004年第4期342-344,共3页Journal of Shanxi University(Natural Science Edition)

基　　金：国家自然科学基金(10371068);山西省自然科学基金(20041003)

摘　　要：讨论了半序集和半序拓扑空间中保序集值算子的最小与最大不动点的存在性.在半序集上,给出了类似于文[2]中关于序Banach空间中混合单调算子的耦合拟不动点的结果;在半序拓扑空间中,改造了文[1]中相关定理中关于算子的条件,得到算子存在最小与最大不动点.The existence of the minimal and maximal fixed points for order preserving set-valued operators on semi-ordered sets and semi-ordered topological spaces was analyzed.The results on semi-ordered sets presented are similar to that of [2] concerning the coupled quasifixed points of mixed monotone multifunction in ordered Banach space.Compared with the results on semi-ordered topological spaces with the relevent theorem in [1],the conditions of the operators are changed,while the assertions are strong relatively.

关 键 词：半序集 半序拓扑空间 保序集值算子 最小与最大不动点 

分 类 号：O177.91[理学—数学]