Rado不等式的多参数推广及应用

通过引入加权幂平均以及参数α、β、μ建立一个新的R ado型不等式,由于所得不等式中含多个参数,因此是一个非常广泛的结果,可以通过对参数的适当取值得到一些已知结果的改进(如著名的Popov iciu不等式的改进),同时也可获得许多新的不等式.最后,我们应用所得结果给出加权幂平均不等式以及加权平均不等式的加细形式.     

(1,k)-configurations and facets for packing problems

A new class of facets for knapsack polytopes is obtained. This class of inequalities is shown to define a polytope with zero–one vertices only. A combinatorial inequality is obtained from Fulkerson's max—max inequality.     

Matrix versions of the Cauchy and Kantorovich inequalities

Summary A version of Cauchy's inequality is obtained which relates two matrices by an inequality in the sense of the Loewner ordering. In that ordering a symmetric idempotent matrix is dominated by the identity matrix and this fact yields a simple proof.A consequence of this matrix Cauchy inequality leads to a matrix version of the Kantorovich inequality, again in the sense of Loewner.     

一个改进的Hardy-Hilbert不等式

通过建立权系数的不等式,得到一个改进的Hardy-Hilbert不等式.     

Fan Ky不等式的一个新改进

利用Gram矩阵的正定性和可变单位向量建立了Fan Ky不等式的一个新的改进,并且建立了反向Fan Ky不等式.对于非奇异矩阵,得到了Fan Ky不等式以及反向Fan Ky不等式的推广.     

Some Improvement on Hilbert''''s Inequality and Its Application

A new improvement of Hilbert's inequality for double series can be established by means of a strengthened Cauchy's inequality. As application, a quite sharp result on Fejer-Riesz's inequality is obtained.     

关于α-凸函数的一个子类的Fekete-Szeg(o)不等式

摘要：引入α-凸函数的一个子类M（α;A,B）,讨论了这个函数类上的Fekete-Szego不等式,得到了准确的结果,推广了一些作者的结果．最后,给出了不等式在利用Hadamard积定义的函数类上的两个应用．     

Interpolating inequalities related to a recent result of Audenaert

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.     

A new integral inequality with power nonlinearity and its discrete analogue

1. IntroductionIt is well known that integral inequalities are very crucial in the study of differelltialequations, integral equations, functional-differential equations, iniegro-differential equationsand evolution equations. Besides the famous Gronwall-Bellman inequality and its first nonlinear generalization due to i. Bihari (of. [1]), there is another very useful integral inequalityestablished by L. On-fang[2]:Lemma 1. Let u(t) and h(t) be real-valued, nonnegative and continuous functions…     

One Inequality for the Moduli of Continuity of Fractional Order Generated by Semigroups of Operators

Ukrainian Mathematical Journal - A new inequality for the moduli of continuity of fractional order generated by semigroups of operators is obtained. This inequality yields a generalization to the...     

Integral Inequalities and Global Solutions of Semilinear Evolution Equations

A criterion for the nonexplosion of solutions to semilinear evolution equations on Banach spaces is proved. The result is obtained by applying a modification of the Bihari type inequality to the case of a weakly singular nonlinear integral inequality.     

Fuzzy Chebyshev type inequality

A Chebyshev type inequality for Sugeno integral is shown. Previous results of Flores-Franulič and Román-Flores [A. Flores-Franulič, H. Román-Flores, A Chebyshev type inequality for fuzzy integrals, Applied Mathematics and Computation 190 (2007) 1178–1184] are generalized. Several illustrated examples are given. As an application, a fuzzy Stolarsky’s inequality is obtained.     

A set-valued type inequality system

A set-valued type inequality system is introduced along with two solvability questions composed of existence and perturbation, and main theorems are obtained, which include three necessary and sufficient conditions concerning the existence and a continuity property concerning the perturbation. As applications, two existence criteria with respect to a single-valued type inequality system have also been obtained.     

Lipschitz函数空间的John-Nirenberg不等式及其应用

本文证明了R~n上Lipschitz函数空间的John-Nirenberg不等式,由此得到了Lipschitz函数空间的一些新的范数等价刻划。此外还对Lipschitz函数空间的定义进行了弱化。     

Mean dual and harmonic cross-sectional measures

Summary The mean dual cross-sectional measures are introduced. They are shown to satisfy a cyclic inequality similar to that satisfied by the cross-sectional measures (Quermassintegrale). A new representation of the dual cross-sectional measures is used to obtain inequalities relating the mean dual cross-sectional measures and the harmonic cross-sectional measures (Harmonische Quermassintegrale) of Hadwiger. An inequality between the volume and the harmonic cross-sectional measures of a convex body is presented. An inequality stronger than the Urysohn inequality (the harmonic Urysohn inequality) is proven. Strengthened versions of other inequalities previously obtained by the author are also presented. Entrata in Redazione il 13 luglio 1977.     

Cauchy-Schwarz不等式的一些反向及改进

在一些附加条件下给出内积空间的Cauchy-Schwarz不等式的反向不等式及其改进,利用所得结果得到一个新的积分型Kantorovich不等式,并获得关于函数的Fourier系数的两个不等式.     

Fan Ky不等式的一个改进

利用改进的H lder不等式并借助于正交矩阵的行列式的积分表示法建立了Fan K y不等式的一个有意义的改进.当A,B为n阶非奇异矩阵时,给出了新创建不等式的一个推广.特别当n=1时,得到了Y oung不等式的一个很强的结果.     

The Local Trace Inequality for Potential Type Integral Operators

The local trace inequality for potential type integral operator is shown and the trace inequality in the framework of Morrey spaces is obtained. A sufficient condition for the equivalence between the Kerman–Sawyer condition and the Adams condition is also presented.     

The Virtual Element Method for an Elliptic Hemivariational Inequality with Convex Constraint

An abstract framework of numerical method is devised for solving an elliptic hemivariational inequality with convex constraint. Convergence of the method is explored under the minimal solution regularity available from the well-posedness of the hemivariational inequality. A Céa-type inequality is derived for error estimation. As a typical example, a virtual element method is proposed to solve a frictionless unilateral contact problem and its optimal error estimates are obtained as well. Numerical results are reported to show the performance of the proposed method.     

Mixed width-integrals of convex bodies

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.