concave-convex function

This article presents the definition of binary convex function,proves that the binary convex function in open and convex region must be continuous,popularizes Jensen s inequality and establishes the decision theorem of binary convex function.

该文给出了二元凸函数的定义,证明了开凸区域上的二元凸函数必连续,推广了Jensen不等式,建立了二元凸函数的判定定理。

This article popularizes the single-dimensional random variable f≤Ef(ξ)(f(x) as convex and concave function into the multi-dimentional scope;therefore concludes a series of important inequalties esp,to convex and concave functions.

将一维随机变量的性质ｆ（Ｅξ）≤Ｅｆ（ξ），（ｆ（ｘ）为凸函数）推广到多维，以此统一推广了一类重要的不等式，对一个非凹凸函数给出了相关的不等式。

Exact Multiplicity of Semi-linear Differential Equations' Solutions Involving Concave-convex Functions

含凹凸函数的半线性微分方程解的确切个数

Application of the Nature of Concave-convex Function in the Proof of Inequality

凹凸函数的性质在不等式证明中的应用

From the basic inequality of concaveconvex function, this paper extends the basic inequality and solves the problems of some inequalities.

从凹凸函数的基本不等式出发,将其推广,可解决某些不等式问题。

An Extension of Differential Mid- Value Theory in Concave (Convex) Functions;

微分中值定理在凹(凸)函数中的推广

An empirical Green function approach with asperity model considered

考虑凹凸体理论的经验格林函数方法

Proof of a Type of Triangle Inequality by Means of Concavo-Convex Function;

利用函数的凹凸性证明一类三角不等式

A Reextension on the Concave-conves of Function through Formula of Taylor;

用泰勒公式研究函数凹凸性的一种再拓广

An Extensiveness on the Concave-convex Property of Function through Formula of Taylor;

用泰勒公式研究函数凹凸性的一种拓广

Alternative characterization of concave and convex functions which is sometimes useful.

对于凹函数和凸函数还有一个替补的表征，有时它是有用的。

The Properties and Applications of Several Classes of Generalized Convex Functions and Convexification, Concavification Method for Monotone Optimization;

几类广义凸函数的性质和应用及单调规划的凸化、凹化方法

Relation between Geometric Convex Function, Square Convex Function and Convex Function;

几何凸函数平方凸函数与凸函数的关系

Continuity, Convexity, Analyticity and Stability of Solutions for Some Iterative Functional Equations;

几类迭代函数方程解的连续性、凹凸性、解析性与稳定性

(2) On the effect boundary, risk is return's rigid monotony increase by degrees convex function , return is risk's rigid monotony increase by degrees concave function.

(2)在有效前沿上,风险是收益的严格单调递增凸函数,收益是风险的严格单调递增凹函数。

STRONGLY PREQUASI-INVEX FUNCTIONS AND STRONGLY QUASI-INVEX FUNCTIONS;

强预拟不变凸函数与强拟不变凸函数

On level sets of E-convex function and E-quasiconvex function

有关E-凸函数和E-拟凸函数的水平集

On E-convex sets,E-convex functions and semi-E-convex functions;

关于E-凸集,E-凸函数和半-E-凸函数性质的研究

Coefficients of some classes of star like and convex functions of order ρ

某些ρ级星形函数和凸形函数的系数

The Relationships between Prequasiinvex Functions and Semi-Continuous Functions

预拟不变凸函数与半连续函数的关系