scholarly journals On a more accurate Hilbert-type inequality in the whole plane with the general homogeneous kernel

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Xingshou Huang ◽  
Bicheng Yang
Keyword(s):  
Equivalent Form ◽  
Type Inequality ◽  
Constant Factor ◽  
Real Analysis ◽  
Homogeneous Kernel ◽  
Hilbert’S Inequality ◽  
The Best Possible Constant ◽  
Hilbert Type ◽  
Weight Coefficients

AbstractBy the use of the weight coefficients, the idea of introduced parameters and the technique of real analysis, a more accurate Hilbert-type inequality in the whole plane with the general homogeneous kernel is given, which is an extension of the more accurate Hardy–Hilbert’s inequality. An equivalent form is obtained. The equivalent statements of the best possible constant factor related to several parameters, the operator expressions and a few particular cases are considered.

scholarly journals A Half-Discrete Hilbert-Type Inequality in the Whole Plane with Multiparameters

2016 ◽  
Vol 2016 ◽  
pp. 1-9 ◽  
Author(s):  
Qunwei Ma ◽  
Bicheng Yang ◽  
Leping He
Keyword(s):  
Type Inequality ◽  
Constant Factor ◽  
Weight Functions ◽  
Real Analysis ◽  
The Best Possible Constant ◽  
Hilbert Type

By the use of weight functions and technique of real analysis, a new half-discrete Hilbert-type inequality in the whole plane with multiparameters and the best possible constant factor is given. Furthermore, the equivalent forms, two kinds of particular inequalities, and the operator expressions with the norm are considered.

scholarly journals A reverse Hilbert-type inequality with a generalized homogeneous kernel

2011 ◽  
Vol 42 (1) ◽  
pp. 1-7
Author(s):  
Bing He
Keyword(s):  
Weight Function ◽  
Integral Inequality ◽  
Equivalent Form ◽  
Type Inequality ◽  
Constant Factor ◽  
Homogeneous Kernel ◽  
Best Constant ◽  
Type Integral ◽  
Best Constant Factor ◽  
Hilbert Type

Inthispaper,by introducing a generalized homogeneous kernel and estimating the weight function,a new reverse Hilbert-type integral inequality with some parameters and a best constant factor is established.Furthermore, the corresponding equivalent form is considered.

scholarly journals On a reverse Mulholland-type inequality in the whole plane with general homogeneous kernel

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Ricai Luo ◽  
Bicheng Yang ◽  
Xingshou Huang
Keyword(s):  
Type Inequality ◽  
Constant Factor ◽  
Homogeneous Kernel ◽  
The Best Possible Constant ◽  
Weight Coefficients

AbstractBy using the idea of introducing parameters and weight coefficients, a new reverse discrete Mulholland-type inequality in the whole plane with general homogeneous kernel is given, which is an extension of the reverse Mulholland inequality. The equivalent forms are obtained. The equivalent statements of the best possible constant factor related to several parameters and a few applied examples are presented.

scholarly journals On a Parametric Mulholland-Type Inequality and Applications

2019 ◽  
Vol 2019 ◽  
pp. 1-8
Author(s):  
Bicheng Yang ◽  
Meifa Huang ◽  
Yanru Zhong
Keyword(s):  
Equivalent Form ◽  
Type Inequality ◽  
Constant Factor ◽  
Weight Functions ◽  
Homogeneous Kernel ◽  
The Best Possible Constant

In this paper, by the use of the weight functions, and the idea of introducing parameters, a discrete Mulholland-type inequality with the general homogeneous kernel and the equivalent form are given. The equivalent statements of the best possible constant factor related to a few parameters are provided. As applications, the operator expressions and a few particular examples are considered.

scholarly journals A Hilbert-Type Integral Inequality with the Homogeneous Kernel of Degree-3 and a Best Constant Factor

2012 ◽  
Vol 4 ◽  
pp. 41-46 ◽  
Author(s):  
Zi Tian Xie ◽  
Zeng Zheng
Keyword(s):  
Weight Function ◽  
Integral Inequality ◽  
Equivalent Form ◽  
Type Inequality ◽  
Constant Factor ◽  
Homogeneous Kernel ◽  
Best Constant ◽  
Type Integral ◽  
Best Constant Factor ◽  
Hilbert Type

By establishing the weight function, we present a new Hilbert-type inequality with the integral in whole plane and with a best constant factor, and its kernel is a homogeneous form of degree-3, and also we put forward its equivalent form.

scholarly journals A New Hilbert-type integral inequality with a non-homogeneous kernel and its extension

2016 ◽  
Vol 4 (3) ◽  
pp. 10
Author(s):  
Weiliang Wu
Keyword(s):  
Weight Function ◽  
Integral Inequality ◽  
Equivalent Form ◽  
Constant Factor ◽  
Real Analysis ◽  
Homogeneous Kernel ◽  
Best Value ◽  
Type Integral ◽  
Hilbert Type

By introducing some parameters , using the weight function and the technique of real analysis, a new  Hilbert-type integral inequality with a non-homogeneous kernel as \(\frac{1}{|1-axy|^{\lambda_2}}(a\geq1)\) and its equivalent form are established. As application, the constant factor on the plane is the best value and its extension form with some parameters is also considered.

scholarly journals A Hardy–Hilbert-Type Inequality Involving Parameters Composed of a Pair of Weight Coefficients with Their Sums

Mathematics ◽  
2021 ◽  
Vol 9 (22) ◽  
pp. 2950
Author(s):  
Bicheng Yang ◽  
Shanhe Wu ◽  
Xingshou Huang
Keyword(s):  
Type Inequality ◽  
Constant Factor ◽  
The Best Possible Constant ◽  
Equivalent Conditions ◽  
Hilbert Type ◽  
Weight Coefficients

In this paper, we establish a new Hardy–Hilbert-type inequality involving parameters composed of a pair of weight coefficients with their sum. Our result is a unified generalization of some Hardy–Hilbert-type inequalities presented in earlier papers. Based on the obtained inequality, the equivalent conditions of the best possible constant factor related to several parameters are discussed, and the equivalent forms and the operator expressions are also considered. As applications, we illustrate how the inequality obtained can generate some new Hardy–Hilbert-type inequalities.

scholarly journals A reverse Hardy–Hilbert-type integral inequality involving one derivative function

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Qian Chen ◽  
Bicheng Yang
Keyword(s):  
Integral Inequality ◽  
Beta Function ◽  
Equivalent Form ◽  
Constant Factor ◽  
Weight Functions ◽  
Derivative Function ◽  
The Best Possible Constant ◽  
Type Integral ◽  
Hilbert Type ◽  
Hilbert Integral

AbstractIn this article, by using weight functions, the idea of introducing parameters, the reverse extended Hardy–Hilbert integral inequality and the techniques of real analysis, a reverse Hardy–Hilbert-type integral inequality involving one derivative function and the beta function is obtained. The equivalent statements of the best possible constant factor related to several parameters are considered. The equivalent form, the cases of non-homogeneous kernel and some particular inequalities are also presented.

scholarly journals On a New Half-Discrete Hilbert-Type Inequality Involving the Variable Upper Limit Integral and Partial Sums

Mathematics ◽  
2020 ◽  
Vol 8 (2) ◽  
pp. 229 ◽  
Author(s):  
Jianquan Liao ◽  
Shanhe Wu ◽  
Bicheng Yang
Keyword(s):  
Type Inequality ◽  
Constant Factor ◽  
Partial Sums ◽  
Upper Limit ◽  
The Best Possible Constant ◽  
Special Case ◽  
Equivalent Conditions ◽  
Hilbert Type

In this paper we establish a new half-discrete Hilbert-type inequality involving the variable upper limit integral and partial sums. As applications, an inequality obtained from the special case of the half-discrete Hilbert-type inequality is further investigated; moreover, the equivalent conditions of the best possible constant factor related to several parameters are proved.

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