在非线性分式函数的情况下广义凸之间的关系

Relationship Between Generalized E-Convex Under the Condition of Nonlinear Fractional Function

在E-凸函数,拟-E-凸函数,伪-E-凸函数的基础上,给出了B-E-凸函数,拟-B-E-凸函数,伪-B-E-凸函数概念;在非线性分式函数的情况下,进一步研究了广义凸之间的9个关系及2个结论;最后对上面的关系及结论给出了4个定理,并用E-凸函数和B-E-凸函数的相关知识分别对其进行了证明。

Firstly,On the basis of E-convex function,quasi-E-convex function,pseudo-E-convex function,I gave B-E-convex function,quasi-B-E-convex function and pseudo-B-E-convex function concept;secondly,At the case of the nonlinear fractional function,was studied nine kinds of relationship and two conclusions between generalized convex was studied;finally,four theorems was given on the base of the above relationship and the conclusion,and tnose tneorems was proved through related knowledge of the E-convex function and B-E convex function.