In this paper, we establish several new Hilbert-type inequalities with a homogeneous kernel, involving arithmetic, geometric, and harmonic mean operators in both integral and discrete case. Such inequalities are deriv...In this paper, we establish several new Hilbert-type inequalities with a homogeneous kernel, involving arithmetic, geometric, and harmonic mean operators in both integral and discrete case. Such inequalities are derived by virtue of some recent results regarding general Hilbert-type inequalities and some well-known classical inequalities. We also prove that the constant factors appearing in established inequalities are the best possible. As an application, we consider some particular settings and compare our results with previously known from the literature.展开更多
In this paper, some new generalizations of inverse type Hilbert-Pachpatte integral inequalities are proved. The results of this paper reduce to those of Pachpatte (1998, J. Math. Anal. Appl. 226, 166–179) and Zhao an...In this paper, some new generalizations of inverse type Hilbert-Pachpatte integral inequalities are proved. The results of this paper reduce to those of Pachpatte (1998, J. Math. Anal. Appl. 226, 166–179) and Zhao and Debnath (2001, J. Math. Anal. Appl. 262, 411–418).展开更多
By introducing some parameters and estimating the weight function, we obtain a reverse Hilbert’s type inequality with the best constant factor. As its applications, we build its equivalent form and some particular re...By introducing some parameters and estimating the weight function, we obtain a reverse Hilbert’s type inequality with the best constant factor. As its applications, we build its equivalent form and some particular results.展开更多
Let Ak be an integral operator defined by Akf（x）：=1K（x）∫Ω2k（x,y）f（y）dμ2（y）where k：Ω1× Ω2 →Ris a general nonnegative kernel, （Ω1,∑1,μ1）, （Ω2,∑2,μ2） are measure spaces with a-finite meas...Let Ak be an integral operator defined by Akf（x）：=1K（x）∫Ω2k（x,y）f（y）dμ2（y）where k：Ω1× Ω2 →Ris a general nonnegative kernel, （Ω1,∑1,μ1）, （Ω2,∑2,μ2） are measure spaces with a-finite measures and K（x）：=∫Ω2k（x,y）dμ2（y）,x∈Ω1.In this paper improvements and reverses of new weighted Hardy type inequalities with integral operators of such type are stated and proved. New Cauchy type mean is introduced and monotonicity property of this mean is proved.展开更多
文摘In this paper, we establish several new Hilbert-type inequalities with a homogeneous kernel, involving arithmetic, geometric, and harmonic mean operators in both integral and discrete case. Such inequalities are derived by virtue of some recent results regarding general Hilbert-type inequalities and some well-known classical inequalities. We also prove that the constant factors appearing in established inequalities are the best possible. As an application, we consider some particular settings and compare our results with previously known from the literature.
文摘In this paper, some new generalizations of inverse type Hilbert-Pachpatte integral inequalities are proved. The results of this paper reduce to those of Pachpatte (1998, J. Math. Anal. Appl. 226, 166–179) and Zhao and Debnath (2001, J. Math. Anal. Appl. 262, 411–418).
基金the Emphases Natural Science Foundation of Guangdong Institutions of Higher Learning,College and University (No.05Z026)
文摘By introducing some parameters and estimating the weight function, we obtain a reverse Hilbert’s type inequality with the best constant factor. As its applications, we build its equivalent form and some particular results.
文摘Let Ak be an integral operator defined by Akf（x）：=1K（x）∫Ω2k（x,y）f（y）dμ2（y）where k：Ω1× Ω2 →Ris a general nonnegative kernel, （Ω1,∑1,μ1）, （Ω2,∑2,μ2） are measure spaces with a-finite measures and K（x）：=∫Ω2k（x,y）dμ2（y）,x∈Ω1.In this paper improvements and reverses of new weighted Hardy type inequalities with integral operators of such type are stated and proved. New Cauchy type mean is introduced and monotonicity property of this mean is proved.
