1) quasiconvex function
拟凸函数
1.
In this paper,we have obtained some criteria for strongly quasiconvex funtions,and have given some characteristics among quasiconver functions,strictly quasiconvex functions and stronly quasiconvex functions.
本文主要讨论了拟凸函数、严格拟凸函数及强拟凸函数之间的关系,得到了某些新的结论,推广了文[1]中的几个主要结论。
2.
Some errors that come from the related literatures were pointed out and corrected,and some properties and determinant criterion of E-quasiconvex functions were provided.
指出相关文献中讨论E-拟凸函数及其性质时出现的一些错误,并作了相应的更正。
3.
Some new properties of explicitly quasiconvex functions are presented in this paper.
提出了显拟凸函数的若干新性质。
2) quasiconvex functions
拟凸函数
1.
[1],Yang presented characterizations of quasiconvex functions,strictly quasiconvex functions,and strongly quasiconvex functions respectively under a certain set of conditions.
在文献[1]中,杨新民教授分别介绍了拟凸函数、严格拟凸函数和强拟凸函数的一些特性,以及它们在一定条件下的性质。
2.
The author proves that a closed weakly nearly convex set is convex, and some equivalent conditions for quasiconvex functions are obtained by applying the results.
在本文中,作者证明了闭的弱近似凸集是凸集,并用此结论获得了拟凸函数的一些等价条件。
3) quasi-convex functions
拟凸函数
1.
Some second order characteristics of pseudo-convex functions,strictly pseudo-convex functions and quasi-convex functions are given.
定义了一种新的广义 Hessian 矩阵 H_(x_1,x_2)(x),并利用该矩阵对二阶可微广义凸函数——伪凸函数、严格伪凸函数和拟凸函数进行了讨论,得到了它们的一些性质。
4) quasiconvex
拟凸函数
1.
According to the article 1 ,we will give some definitions of quasiconvex function,and discuss their equivalent.
在文献1的基础上,给出了拟凸函数的几种定义形式,并讨论了它们之间的等价关系。
5) quasi convex function
拟凸函数
1.
The integral operator Pσλf(z) was used to describe starlike function,convex function close-to-convex function and the new subclass of quasi convex function and to establish inclusion relations.
用积分算子Pσλf(z)刻划了星象函数,凸象函数,近于凸函数,拟凸函数的新子类,建立了包含关系。
6) strongly quasiconvex functions
强拟凸函数
1.
[1],Yang presented characterizations of quasiconvex functions,strictly quasiconvex functions,and strongly quasiconvex functions respectively under a certain set of conditions.
在文献[1]中,杨新民教授分别介绍了拟凸函数、严格拟凸函数和强拟凸函数的一些特性,以及它们在一定条件下的性质。
补充资料:凸函数
Image:11559688111252300.jpg
凸函数是一个定义在某个向量空间的凸子集c(区间)上的实值函数f
设f为定义在区间i上的函数,若对i上的任意两点x1,x2和任意的实数λ∈(0,1),总有
f(λx1+(1-λ)x2)≤λf(x1)+(1-λ)f(x2),
则f称为i上的凸函数.
判定方法可利用定义法、已知结论法以及函数的二阶导数
说明:补充资料仅用于学习参考,请勿用于其它任何用途。