共查询到20条相似文献,搜索用时 31 毫秒
1.
关于两个新型Hilbert不等式的推广 总被引:10,自引:2,他引:8
众所周知,Hilbert不等式是一个有重要应用的不等式,1998年,B.G.Pachpatte给出了类似Hilbert级数不等式的两个新不等式,本文的主要工作是推广了这两个新个新不等式。 相似文献
2.
B. G. Pachpatte 《Periodica Mathematica Hungarica》1987,18(2):137-141
In the present paper we establish two new integral inequalities similar to Opial's inequality in two independent variables. The inequalities established in this paper are similar to the analogues of Calvert's generalizations of Opial's inequality, in two independent variables and contains in the special case the analogue of Opial's inequality given by G. S. Yang in two independent variables. 相似文献
3.
In this paper, we study classical Hardy inequalities, both in the subcritical case on the whole space and the critical case on a ball. Two Hardy inequalities are quite different from each other in view of their forms, scaling structures and optimal constants. Nevertheless we show that, when the exponents are chosen appropriately, both inequalities are equivalent at least in the radial setting. A transformation which connects two inequalities is a key in our argument. As an application, we improve the critical Hardy inequality on a ball by using the improved subcritical inequality on the whole space. 相似文献
4.
Redundant constraints in linear inequality systems can be characterized as those inequalities that can be removed from an
arbitrary linear optimization problem posed on its solution set without modifying its value and its optimal set. A constraint
is saturated in a given linear optimization problem when it is binding at the optimal set. Saturation is a property related
with the preservation of the value and the optimal set under the elimination of the given constraint, phenomena which can
be seen as weaker forms of excess information in linear optimization problems. We say that an inequality of a given linear
inequality system is uniformly saturated when it is saturated for any solvable linear optimization problem posed on its solution
set. This paper characterizes the uniform saturated inequalities and other related classes of inequalities.
This work was supported by the MCYT of Spain and FEDER of UE, Grant BFM2002-04114-C02-01. 相似文献
5.
Ta Lê Loi 《manuscripta mathematica》2016,150(1-2):59-72
This note is devoted to the generalization of ?ojasiewicz inequalities for functions definable in o-minimal structures, which is, roughly speaking, a generalization for semialgebraic or global subanalytic functions. We present some o-minimal versions of the inequalities to compare two definable functions globally or in some neighborhoods of the zero-sets of the functions, and the gradient inequalities (Kurdyka–?ojasiewicz inequality and Bochnak–?ojasiewicz inequality). Some applications of the inequalities are given. 相似文献
6.
证明了半序线性空间上线性泛函的两个Gr\"{u}ss型不等式, 并由此给出了Karamata型积分不等式的一种推广形式,
得到了一个新的Gr\"{u}ss型积分不等式及关于傅立叶系数的两个不等式.
最后利用所得结论研究了关于矩阵及线性算子的一些Gr\"{u}ss型不等式. 相似文献
7.
In this paper, the Minty vector variational-like inequality, the Stampacchia vector variational-like inequality, and the weak formulations of these two inequalities defined by means of Mordukhovich limiting subdifferentials are introduced and studied in Asplund spaces. Some relations between the vector variational-like inequalities and vector optimization problems are established by using the properties of Mordukhovich limiting subdifferentials. An existence theorem of solutions for the weak Minty vector variational-like inequality is also given. 相似文献
8.
9.
A purely analytic proof is given for an inequality that has as a direct consequence the two most important affine isoperimetric
inequalities of plane convex geometry: The Blaschke-Santaló inequality and the affine isoperimetric inequality of affine differential
geometry. 相似文献
10.
针对一类时滞不确定中立型分布参数系统,研究该系统基于线性矩阵不等式方法的稳定性判据.基于线性矩阵不等式(LMI)方法,通过构造一系列适当的李雅普诺夫函数,利用散度定理和矩阵不等式技术,给出了系统是渐近稳定的充分条件.充分条件要求满足两个线性矩阵不等式,而线性矩阵不等式容易利用Matlab中的LMI工具箱进行求解.最后,数值算例验证了该方法的有效性. 相似文献
11.
Jie Xiao 《Advances in Mathematics》2007,211(2):417-435
This paper shows that each of the sharp (endpoint) Sobolev inequality and the isoperimetric inequality can be split into two sharp and stronger inequalities through either the 1-variational capacity or the 1-integral affine surface area. Furthermore, some related sharp analytic and geometric inequalities are also explored. 相似文献
12.
Rasul A. Khan 《Journal of Theoretical Probability》2009,22(2):348-364
The Dubins–Savage inequality is generalized by using the pth (1<p≤2) conditional moment of the martingale differences. This inequality is further extended under suitable conditions when p>2. Another martingale inequality due to Freedman is also generalized when 0<p≤2. Implications of these inequalities for strong convergence are discussed. Some general exponential inequalities are also
given for martingales (supermartingales) under suitable conditions.
相似文献
13.
In this paper, we explore conditions under which certain elliptic hemivariational inequalities permit equivalent minimization principles. It is shown that for an elliptic variational–hemivariational inequality, under the usual assumptions that guarantee the solution existence and uniqueness, if an additional condition is satisfied, the solution of the variational–hemivariational inequality is also the minimizer of a corresponding energy functional. Then, two variants of the equivalence result are given, that are more convenient to use for applications in contact mechanics and in numerical analysis of the variational–hemivariational inequality. When the convex terms are dropped, the results on the elliptic variational–hemivariational inequalities are reduced to that on “pure” elliptic hemivariational inequalities. Finally, two representative examples from contact mechanics are discussed to illustrate application of the theoretical results. 相似文献
14.
K. K. CHONG 《数学年刊A辑(中文版)》2002,(1):75-84
Refinements to inequalities on inner product spaces are presented. In this respect, inequalities dealt with in this paper are: Cauchy's inequality, Bessel's inequality, Fan-Todd's inequality and Fan-Todd's determinantal inequality. In each case, a strictly increasing function is put forward, which lies between the smaller and the larger quantities of each inequality. As a result, an improved condition for equality of the Fan-Todd's determinantal inequality is deduced. 相似文献
15.
Chia Shiang Lin 《数学学报(英文版)》2001,17(4):657-668
In this paper we initiate a study of covariance and variance for two operators on a Hilbert space, proving that the c-v (covariance-variance)
inequality holds, which is equivalent to the Cauchy-Schwarz inequality. As for applications of the c-v inequality we prove
uniformly the Bernstein-type inequalities and equalities, and show the generalized Heinz-Kato-Furuta-type inequalities and
equalities, from which a generalization and sharpening of Reid's inequality is obtained. We show that every operator can be
expressed as a p-hyponormal-type, and a hyponormal-type operator. Finally, some new characterizations of the Furuta inequality are given.
Received April 9, 2000, Revised July 20, 2000, Accepted August 8, 2000 相似文献
16.
O.S Rothaus 《Journal of Functional Analysis》1985,64(2):296-313
There is a simple equivalence between isoperimetric inequalities in Riemannian manifolds and certain analytic inequalities on the same manifold, more extensive than the familiar equivalence of the classical isoperimetric inequality in Euclidean space and the associated Sobolev inequality. By an isoperimetric inequality in this connection we mean any inequality involving the Riemannian volume and Riemannian surface measure of a subset α and its boundary, respectively. We exploit the equivalence to give log-Sobolev inequalities for Riemannian manifolds. Some applications to Schrödinger equations are also given. 相似文献
17.
研究了关于Lp混合均值积分的log-Minkowski不等式,应用Jensen不等式给出Lp混合均值积分的log-Minkowski不等式的简化证明,同时应用加强的Jensen不等式给出一加强不等式. 相似文献
18.
S. S. Dragomir 《Linear and Multilinear Algebra》2017,65(3):514-525
A Buzano type inequality for two nonnegative Hermitian forms is obtained. Applications to inequalities for norm and numerical radius of bounded linear operators in complex Hilbert spaces are given. 相似文献
19.
Inequalities are an important topic in school mathematics, yet the body of research exploring students’ meanings for inequalities largely points to difficulties they experience. Thus, there is a need to further explore students’ meanings for inequalities. Addressing this need, we conducted an exploratory teaching experiment with two seventh-grade students to investigate their developing meanings for inequalities. We distinguish between two types of inequalities in student thinking: comparative and restrictive inequalities. Whereas a student reasoning about a comparative inequality compares two quantities’ values or magnitudes, reasoning about a restrictive inequality entails reasoning about a range of one quantity’s magnitudes or values. We realized a complexity arose in our interactions with students due to our conceiving the use of inequality symbols across the two types of inequalities as polysemous, whereas the students did not. Attending to these two types of inequalities has important implications for the teaching and learning of inequality. 相似文献
20.
Several new inequalities are obtained for the modulus, the real part, and the imaginary part of a linear combination of the ordered eigenvalues of a square complex matrix. Included are bounds for the condition number, the spread, and the spectral radius. These inequalities involve the trace of a matrix and the trace of its square. Necessary and sufficient conditions for equality are given for each inequality. 相似文献