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

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.