常见的代数不等式的证明

给出了利用导数证明常见的几种代数不等式的基本方法,并对J.B.W ilke不等式给出了一个简单的证明     

L^2空间中的Bernstein—Markov不等式及其最佳常数

1 引言 设-∞≤a相似文献   

多元Newman不等式与逼近逆定理

本文研究多元有理逼近的Newman不等式与逼近逆定理问题.在多元Müntz多项式空间中利用分解方法建立多元有理多项式的Markov型不等式与Nikolskii型不等式.同时,建立多元有理逼近的逆定理,即Steckin型不等式.本文所获结果不仅推广了一元的相应结果,而且包含了关于代数多项式的一些经典结果.     

Hlder不等式和Minkowski不等式的推广

本文利用变分方法对多个变元的不含变元导数的H■lder不等式和Minkowski不等式进行了推广．此种方法的主要意义不在于证明传统的不等式,而在于发现新的不等式．     

Hlder不等式和Minkowski不等式的推广

本文利用变分方法对多个变元的不含变元导数的Holder不等式和Minkowski不等式进行了推广．此种方法的主要意义不在于证明传统的不等式，而在于发现新的不等式．     

利用导数运算法则构造函数解问题

给出含有导数式子的等式或不等式，判断一类等式或不等式是否成立，这类问题常常需要利用导数的运算法则构造函数，然后利用导函数的性质解决问题．下面我们举例说明．     

一类含中介值定积分等式证明题的构造

利用多项式插值理论,结合数值求积公式代数精度的概念,给出了一种构造和证明一类含中介值定积分等式证明题的新方法,并给出多个应用实例.     

Abel不等式和Hlder不等式的一个共同加强

在本篇短文中,我们将利用Young不等式建立一个代数不等式,所给的证明是十分简洁的.并且我们将看到这个代数不等式是著名的Abel不等式和H(o)lder不等式的一个共同加强.     

插值三角多项式在Orlicz空间逼近的渐进等式

对于具有等距分布插值结点的三角多项式,借助广义的Minkowski不等式在Orlicz空间内建立了由三角多项式逼近的渐近等式.并对于Orlicz空间内不同的函数类给出不同的结果.     

分析变换代数结构的途径与方法

在高中代数教学中,数学思想方法的发现往往在问题的深入中展开．而多项式是最常见的代数结构,本文试以多项式中常见的元素在学习、解题过程中的处理及意义出发,分析代数结构变换的一般思路与方法．     

An Estimate of a Polynomial Capacity

We prove an estimate of a polynomial capacity for sets preserving Markov's inequality. Our estimate reflects some of the algebraic properties of these sets.     

О прямых и обратных те оремах теории аппроксимаци и в метрике знакочувст вительного веса

The following results are obtained for the metric of a sign sensitive weight: necessary and sufficient conditions imposed on the weight in order to ensure the fulfillment of the complete analogue of Jackson's theorem on the estimate of the best approximation of an arbitrary continuous function by means of its modulus of continuity; the analogue of Bernstein's inequality on the estimate of the derivative of a trigonometric polynomial; the analogue of Stechkin's theorem on the connection between the modulus of continuity of a function and the rate of its approximation by polynomials; the analogue of Dolzhenko's inequality on the estimate of the variation of a rational function; and the analogue of Dolzhenko's theorem on the estimate of the variation of a function by means of its best rational approximation.     

Higher order Ostrowski type inequalities over Euclidean domains

The classical Ostrowski inequality for functions on intervals estimates the value of the function minus its average in terms of the maximum of its first derivative. This result is extended to functions on general domains using the L^∞ norm of its nth partial derivatives. For radial functions on balls the inequality is sharp.     

二次可微函数的Ostrowski型不等式

研究了一类二次可微函数,利用二阶导数的上界和下界,给出了二次可微函数的O strow sk i型不等式,同时也推广了经典的中点不等式和梯形不等式.     

Extension of Bernstein's theorem for polynomial maps of complex Banach spaces

Bernstein's inequality (1) will be extended to polynomial maps of arbitrary complex Banach spaces; cf. (3). We also give conditions for equality in (3). The extension of Bernstein's inequality to the case of polynomial maps of ℂ into ℂ was given byTung [4] and [5].     

Signorini接触问题的边界变分不等式

本以Signorini接触问题为背景，讨论了变分不等式与边值问题的等价性，利用Green公式，基本解和基本解法向导数的性质，将区域型变分不等式化成等价的边界型变分不等式，并证明了边界变分不等式解的存在唯一性，为使用边界元方法数值求解提供理论依据。     

关于三个未解决的不等式问题

通过求二阶导数或列举反例的方法可解决《常用不等式（第四版）》末尾提出的问题3、问题13和问题62,另外,利用Lyapunov不等式及Moran不等式可给出其问题190中一个不等式的下界.     

Heinz's inequality and Bernstein's inequality

The purpose of the present account is to sharpen Heinz's inequality, and to investigate the equality and the bound of the inequality. As a consequence of this we present a Bernstein type inequality for nonselfadjoint operators. The Heinz inequality can be naturally extended to a more general case, and from which we obtain in particular Bessel's equality and inequality. Finally, Bernstein's inequality is extended to eigenvectors, and shows that the bound of the inequality is preserved.

     

Simpson不等式的改进及其应用

通过一阶导数对Simpson不等式进行了改进,并推导出了相应的数值积分公式和最佳误差限,扩大了Simpson积分公式的适用范围,最后给出了具体的数值应用.     

Subdifferential estimate of the directional derivative,optimality criterion and separation principles

We provide an inequality relating the radial directional derivative and the subdifferential of proper lower semicontinuous functions, which extends the known formula for convex functions. We show that this property is equivalent to other subdifferential properties of Banach spaces, such as controlled dense subdifferentiability, optimality criterion, mean value inequality and separation principles. As an application, we obtain a first-order sufficient condition for optimality, which extends the known condition for differentiable functions in finite-dimensional spaces and which amounts to the maximal monotonicity of the subdifferential for convex lower semicontinuous functions. Finally, we establish a formula describing the subdifferential of the sum of a convex lower semicontinuous function with a convex inf-compact function in terms of the sum of their approximate ?-subdifferentials. Such a formula directly leads to the known formula relating the directional derivative of a convex lower semicontinuous function to its approximate ?-subdifferential.