E-凸函数的若干性质

Some properties of E-convex function

利用E-凸集和E-凸函数的定义,研究了E-凸函数的性质,给出并证明了E-凸函数的一个充分必要条件:设集合MRn,映射E:Rn→Rn,函数f:Rn→R和g:R→R,且g(t)=f(x+td),(其中d∈Rn),则f是E-凸函数当且仅当g是E-凸函数.并对E-凸函数的若干特征进行了研究分析,得出了E-凸函数的判别条件及其性质.

The properties of E- convex function were studied using the definition of E- convex sets and convex function. A necessary and sufficient condition of E- convex function was proved： let MR^n,mapping E： R^n→R^n,function f： R^n→R and g： R→R function,and g（t）= f（ x ＋ td）（ where d∈R^n）,then f is a E- convex function if and only if g is a E- convex function. And several features of E- convex functionwere studied and analyzed. The criterions and properties of E- convex function were obtained.