利用二元函数性质来刻画集值映射的单调性  

Some Characterizations of Monotonicity of Set-valued mappings By Using Properties of Bifunctions

作　　者：龙天友 叶明露[1] 李军[1] 

机构地区：[1]西华师范大学数学与信息学院,四川南充637009

出　　处：《西华师范大学学报（自然科学版）》2016年第3期289-296,共8页Journal of China West Normal University(Natural Sciences)

基　　金：国家自然科学基金项目(11371015);教育部科学技术重点项目(211163);四川省青年科技基金(2012JQ0035)

摘　　要：首先回顾了集值映射和二元函数的几种单调性,包括单调、严格单调、强单调、伪单调、拟单调以及弱单调,并定义了二元集值函数的这几种单调性,同时举出大量例子说明这些单调性之间的关系。最后,利用二元实值函数和二元集值函数的六种单调性分别刻画了集值映射的六种单调性。In this paper, we first recall the monotonicity of set-valued mappings and bifunctions, such as monotonoicity, strict monotonicity, strong monotonicity, pseudomonotonicity, quasimonotonicity and weak monotonicity. We then define these monotonicity of set-valued bifunctions. Several examples are given to illustrate these monotonicity. We also give some new characterizations of six kinds of monotonicity of set-valued mappings by using bifunctions and set-valued bifunctions.

关 键 词：集值映射 二元函数 单调性条件 

分 类 号：O221[理学—运筹学与控制论]