ICR函数与DICR函数的抽象凸性分析

Abstract Convex Analysis of ICR and DICR Functions

在拓扑向量空间中研究函数φ:X×X×R++→[0,+∞],φ(x,y,α):=sup{λ:0≤λ≤α,λx≤y},这里x,y∈X,α∈R_(++)。证明该函数关于第一变元是DICR函数,关于第二变元是ICR函数,并分别研究这两类函数的抽象凸性。

Abstract ： In this paper,the study of φ：X×X×R＋＋→[0,＋∞] function defined by φ（x,y,α）：= sup {λ：0≤λ≤α,λx≤y} , x,y∈X,α∈R（＋＋）is conducted in a topological vector space. Function ~ is proved to be DICR function in the first argument and ICR function in the second argument. In addition,the abstract convexity of both two func- tions is also discussed.