This article emphasizes important application of convex function in inequality proving.
本文着重论述了凸函数在不等式证明中的重要应用。
In this paper, several properties of convex function are generalized to the case of quasi convex function.
本文讨论了将凸函数的几个性质推广到拟凸函数的情形。
In this paper, we give some criteria for convex function, strictly convex function and explicitly convex function.
本文给出了凸函数，严格凸函数和显凸函数的一些判别准则。
An integral property of the convex function is generalized, and the some integral inequalities of the convex function are given.
给出了凸函数的一个积分性质的推广，并由此得到了凸函数的几个积分不等式。
This article gives a spreading form of the mean value theorem of differential and applies the gained results to the quality of convex function.
给出了微分中值定理的一个推广形式，并将所得结果应用于凸函数性质的研究。
It is proved that the optimality conditions are also sufficient if the objective function is a convex function of the plastic limit bending moment.
当目标函数是塑性极限弯矩凸函数时，证明了这一最优性条件也是最优解的充分条件。
There are convex function and concave function, Which are of expansive application in many aspects, especially in inequality proof and error estimate.
凸(凹)函数有很多特性，这些性质可广泛应用于不等式的证明及误差估计等方面。
In this paper, we use the convex function to form the order statistic and the linear rank statistic, and the asymptotic normality of the statistics are proved.
本文用凸函数构造了线性次序统计量和线性秩统计量，并证明了它们的渐近正态性。
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.
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。
As applications of majorizing inequality of convex function of several variables, some majorizing inequalities of eigenvalue and singular value of matrix are obtained.
作为多元凸函数的控制不等式在矩阵方面的初步应用，获得了矩阵特征值和奇异值的简洁的控制不等式。
This paper discusses the relationship between quasi-concave and pseudo-convex in the generalized convex function in the Linear topological space and offers some conditions of equivalence.
讨论了线性拓扑空间上广义凸函数中的拟凸与伪凸之间的关系，并给出它们之间的一些等价条件。
According to the character of expected information, the article proposed a new ID3 algorithm of decision trees to reduce the complexity of computing expected information by the convex function.
根据ID3算法中信息增益计算原理的特点，利用上凸函数的性质提出一种新的改进的ID3算法，减少了信息增益的计算量，进而提高ID3算法中信息增益的计算效率。
The concept of the midpoint quasi-convex function is introduced, and some conditions are obtained to ensure that midpoint quasi-convex function is quasi-convex in the measurable function space.
本文提出了中点拟凸函数的概念，在可测函数空间中，给出了中点拟凸函数拟凸的若干个充分条件。
This paper investigates the existence of complex support functional of a convex function in complex linear spaces and the complex numerical ranges of the complex support functionals on a point.
采用子空间中支撑泛函延拓的方法，构造出在复线性空间任意点上的复支撑泛函；确定在同一支撑点上复支撑泛函的数值域，从而得到复支撑泛函具有唯一性的充分必要条件。
Convex function plays an important role in mathematical programming.
凸函数在数学规划中具有十分重要的作用。
Convex function of demand, convex distribution of price and an optimal model for coexistence of multi-prices are established.
建立了商品销售中的凸需求函数，凸分布和多种价格并存的优化模型。
Convex function of demand, convex distribution of price and an optimal model for coexistence of multi-prices are established.
建立了商品销售中的凸需求函数，凸分布和多种价格并存的优化模型。
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