A delay difference inequality was studied, and several results were obtained, which improve the known results. Then a typical integral inequality with two independent variables was studied, and some results were obtai...A delay difference inequality was studied, and several results were obtained, which improve the known results. Then a typical integral inequality with two independent variables was studied, and some results were obtained, which extend the known results.展开更多
In this paper, it is shown that Hardy-Hilbert＇s integral inequality with parameter is improved by means of a sharpening of Hoeder＇s inequality. A new inequality is established as follows：∫^∞α∫^∞α f（x）g（y）...In this paper, it is shown that Hardy-Hilbert＇s integral inequality with parameter is improved by means of a sharpening of Hoeder＇s inequality. A new inequality is established as follows：∫^∞α∫^∞α f（x）g（y）/（x＋y＋2β）dxdy〈π/sin（π/p）{∫^∞α f^p（x）dx}1/p·{∫^∞αgq（x）dx}1/q·（1-R）^m,where R=（Sp （F, h） - Sq （G, h））^2, m= min （1/p, 1/q）. As application; an extension of Hardy-Littlewood＇s inequality is given.展开更多
The paper brings an important integral inequality, which includes the famous Polya-Szego inequality and the logarithmical-arithmetic mean inequality as special cases.
The main purpose of the present article is to establish some new strengthed and reversed Pachpatte's type inequalities. As applications, some new type Hilbert's inequlities are generalized and strengthened.
Refinements to inequalities on inner product spaces are presented. In this respect, inequali-ties dealt with in this paper are: Cauchy’s inequality, Bessel’s inequality, Fan-Todd’s inequality and Fan-Todd’s determ...Refinements to inequalities on inner product spaces are presented. In this respect, inequali-ties 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 for-ward, 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.展开更多
We investigate the Liouville theorem for an integral system with Poisson kernel on the upper half space R+n,{u（x） =2/（nωn）∫?R+n（xnf（v（y）））/（|x- y|n）dy, x ∈R+n,v（y） =2/（nωn）∫R+n（xng（u（x）））/（...We investigate the Liouville theorem for an integral system with Poisson kernel on the upper half space R+n,{u（x） =2/（nωn）∫?R+n（xnf（v（y）））/（|x- y|n）dy, x ∈R+n,v（y） =2/（nωn）∫R+n（xng（u（x）））/（|x- y|n）dx, y ∈?R+n,where n 3, ωn is the volume of the unit ball in Rn. This integral system arises from the Euler-Lagrange equation corresponding to an integral inequality on the upper half space established by Hang et al.（2008）.With natural structure conditions on f and g, we classify the positive solutions of the above system based on the method of moving spheres in integral form and the inequality mentioned above.展开更多
基金National Natural Science Foundation ofChina( No.1983 10 3 0 )
文摘A delay difference inequality was studied, and several results were obtained, which improve the known results. Then a typical integral inequality with two independent variables was studied, and some results were obtained, which extend the known results.
文摘In this paper, it is shown that Hardy-Hilbert＇s integral inequality with parameter is improved by means of a sharpening of Hoeder＇s inequality. A new inequality is established as follows：∫^∞α∫^∞α f（x）g（y）/（x＋y＋2β）dxdy〈π/sin（π/p）{∫^∞α f^p（x）dx}1/p·{∫^∞αgq（x）dx}1/q·（1-R）^m,where R=（Sp （F, h） - Sq （G, h））^2, m= min （1/p, 1/q）. As application; an extension of Hardy-Littlewood＇s inequality is given.
基金the Scientific Research fund of Pingyuan University(2005006)
文摘The paper brings an important integral inequality, which includes the famous Polya-Szego inequality and the logarithmical-arithmetic mean inequality as special cases.
基金the National Natural Science Foundation of China(10271071)and the Academic Mainstay of Middle-age and Youth Foundation of Shandong Province.
文摘The main purpose of the present article is to establish some new strengthed and reversed Pachpatte's type inequalities. As applications, some new type Hilbert's inequlities are generalized and strengthened.
文摘Refinements to inequalities on inner product spaces are presented. In this respect, inequali-ties 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 for-ward, 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.
基金supported by National Natural Science Foundation of China (Grant No. 11571268)Natural Science Basic Research Plan in Shaanxi Province of China (Grant No. 2014JM1021)
文摘We investigate the Liouville theorem for an integral system with Poisson kernel on the upper half space R+n,{u（x） =2/（nωn）∫?R+n（xnf（v（y）））/（|x- y|n）dy, x ∈R+n,v（y） =2/（nωn）∫R+n（xng（u（x）））/（|x- y|n）dx, y ∈?R+n,where n 3, ωn is the volume of the unit ball in Rn. This integral system arises from the Euler-Lagrange equation corresponding to an integral inequality on the upper half space established by Hang et al.（2008）.With natural structure conditions on f and g, we classify the positive solutions of the above system based on the method of moving spheres in integral form and the inequality mentioned above.
