共查询到20条相似文献,搜索用时 15 毫秒
1.
吴善和 《数学的实践与认识》2005,35(9):134-139
利用Ho。lder不等式、Young不等式、Chebyshev不等式、幂平均不等式建立Radon不等式的指数推广形式,得到一个具有广泛应用价值的不等式.指出文[7]中给出的关于Radon不等式的推广结果是错误的,并在本文中作了修正. 相似文献
2.
Erwin Lutwak 《Israel Journal of Mathematics》1977,28(3):249-253
The mixed width-integrals are defined and shown to have properties similar to those of the mixed volumes of Minkowski. An
inequality is established for the mixed width-integrals analogous to the Fenchel-Aleksandrov inequality for the mixed volumes.
An isoperimetric inequality (involving the mixed width-integrals) is presented which generalizes an inequality recently obtained
by Chakerian and Heil. Strengthened versions of this general inequality are obtained by introducing indexed mixed width-integrals.
This leads to an isoperimetric inequality similar to Busemann’s inequality involving concurrent cross-sections of convex bodies. 相似文献
3.
三大著名不等式的拓广与深化 总被引:1,自引:0,他引:1
利用一个分式型的双向积分不等式 ,将 H lder不等式、H.Minkowski不等式、Schl milch不等式(幂平均不等式 )三大世界著名不等式进行拓广与深化 ,使对此问题的研究更具深刻性、系统性 . 相似文献
4.
5.
李衍禧 《数学的实践与认识》2009,39(11)
实对称正定矩阵的Szasz不等式是Hadamard不等式的加细;本文将Szasz不等式推广到一类亚正定矩阵和拟广义正定矩阵上去,从而推广了关于实对称正定矩阵的Szasz不等式和Hadamard不等式. 相似文献
6.
Anthony Carbery 《Proceedings of the American Mathematical Society》2004,132(11):3141-3152
We prove a multilinear inequality which in the bilinear case reduces to the Cauchy-Schwarz inequality. The inequality is combinatorial in nature and is closely related to one established by Katz and Tao in their work on dimensions of Kakeya sets. Although the inequality is ``elementary" in essence, the proof given is genuinely analytical insofar as limiting procedures are employed. Extensive remarks are made to place the inequality in context.
7.
《Journal of the Egyptian Mathematical Society》2014,22(2):254-257
In this paper, we introduce two new forms of the half-discrete Hilbert inequality. The first form is a sharper form of the half-discrete Hilbert inequality and is related to Hardy inequality. In the second one, we give a differential form of this inequality. 相似文献
8.
研究了代数多项式导数的Bernstein不等式和Markov不等式.通过代数多项式导数的一个积分表示式,给出这两个著名不等式以及它们的离散形式的证明. 相似文献
9.
杨乐不等式的推广及加强 总被引:1,自引:0,他引:1
赵长健 《数学的实践与认识》2000,30(4)
本文首先利用凸函数基本不等式和平均值不等式推广并加强了杨乐不等式 ,然后利用 Jensen不等式给出了两个更为广泛的结果 . 相似文献
10.
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。 相似文献
11.
In this paper we show a new inequality that generalizes to the unit sphere the Lebedev-Milin inequality of the exponentiation of functions on the unit circle. It may also be regarded as the counterpart on the sphere of the second inequality in the Szegö limit theorem on the Toeplitz determinants on the circle. On the other hand, this inequality is also a variant of several classical inequalities of Moser-Trudinger type on the sphere. The inequality incorporates the deviation of the center of mass from the origin into the optimal inequality of Aubin for functions with mass centered at the origin, and improves Onofri's inequality with the contribution of the shifting of the mass center explicitly expressed. © 2021 Wiley Periodicals LLC. 相似文献
12.
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. 相似文献
13.
Milica Klaričić Bakula Marko Matić Josip Pečarić 《Central European Journal of Mathematics》2009,7(4):787-803
We present a couple of general inequalities related to the Jensen-Steffensen inequality in its discrete and integral form.
The Jensen-Steffensen inequality, Slater’s inequality and a generalization of the counterpart to the Jensen-Steffensen inequality
are deduced as special cases from these general inequalities. 相似文献
14.
In this paper, we study strict feasibility of a bifunction variational inequality. It is proved that a monotone bifunction variational inequality has a nonempty and bounded solution set if and only if it is strictly feasible. Stable solvability of the bifunction variational inequality is discussed under strict feasibility assumption when the domain set is perturbed. Our results generalize earlier results on the classical variational inequality to the case of the bifunction variational inequality. 相似文献
15.
张荣 《数学的实践与认识》2007,37(20):224-226
将不等式问题转化为函数问题,利用函数性质来研究、解决不等式问题.掌握不等式证明的一种函数思想方法,从而提高分析问题与解决问题的能力. 相似文献
16.
通过引入带参数的指数积分并利用Bernoulli不等式以及改进了的Hlder不等式,对Hardy-Hilbert积分不等式作了有意义改进.特别,当p=2时,得到了经典的Hilbert积分不等式的一个很强的结果. 相似文献
17.
Mohammad Al-khlyleh 《Linear and Multilinear Algebra》2017,65(5):922-929
Audenaert recently obtained an inequality for unitarily invariant norms that interpolates between the arithmetic–geometric mean inequality and the Cauchy–Schwarz inequality for matrices. A refined version of Audenaert’s inequality for the Hilbert–Schmidt norm is given. Other interpolating inequalities for unitarily invariant norms are also presented. 相似文献
18.
Huriye
Kadakal 《Numerical Methods for Partial Differential Equations》2020,36(6):1555-1565
In this study, using power-mean inequality and improved power-mean integral inequality better approach than power-mean inequality and an identity for differentiable functions, we get inequalities for functions whose derivatives in absolute value at certain power are convex. Numerically, it is shown that improved power-mean integral inequality gives better approach than power-mean inequality. Some applications to special means of real numbers and some error estimates for the midpoint formula are also given. 相似文献
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