scholarly journals A new Hardy–Mulholland-type inequality with a mixed kernel

2021 ◽  
Vol 6 (2) ◽  
Author(s):  
Michael Th. Rassias ◽  
Bicheng Yang ◽  
Andrei Raigorodskii
Keyword(s):  
Hypergeometric Function ◽  
Type Inequality ◽  
Constant Factor ◽  
Real Analysis ◽  
Operator Expression ◽  
Weight Coefficients

AbstractBy the use of weight coefficients and techniques of real analysis, we establish a new Hardy–Mulholland-type inequality with a mixed kernel and a best possible constant factor in terms of the hypergeometric function. Equivalent forms, an operator expression with the norm and reverses are also considered.

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 On an Extension of a Hardy-Hilbert-Type Inequality with Multi-Parameters

Mathematics ◽  
2021 ◽  
Vol 9 (19) ◽  
pp. 2432
Author(s):  
Bicheng Yang ◽  
Michael Th. Rassias ◽  
Andrei Raigorodskii
Keyword(s):  
Type Inequality ◽  
Constant Factor ◽  
Operator Expression ◽  
Analytic Methods ◽  
Hilbert Type ◽  
Weight Coefficients ◽  
Real Complex

Making use of weight coefficients as well as real/complex analytic methods, an extension of a Hardy–Hilbert-type inequality with a best possible constant factor and multiparameters is established. Equivalent forms, reverses, operator expression with the norm, and a few particular cases are also 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 On two kinds of the reverse half-discrete Mulholland-type inequalities involving higher-order derivative function

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Qiang Chen ◽  
Bicheng Yang
Keyword(s):  
Type Inequality ◽  
Higher Order ◽  
Constant Factor ◽  
Order Derivative ◽  
Weight Functions ◽  
Real Analysis ◽  
Derivative Function ◽  
Hadamard’S Inequality ◽  
The Best Possible Constant ◽  
Higher Order Derivative

AbstractBy means of the weight functions, Hermite–Hadamard’s inequality, and the techniques of real analysis, a new more accurate reverse half-discrete Mulholland-type inequality involving one higher-order derivative function is given. The equivalent statements of the best possible constant factor related to a few parameters, the equivalent forms, and several particular inequalities are provided. Another kind of the reverses is also 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 A reverse Mulholland-type inequality in the whole plane with multi-parameters

2019 ◽  
Vol 13 (1) ◽  
pp. 290-308
Author(s):  
Michael Rassias ◽  
Bicheng Yang
Keyword(s):  
Type Inequality ◽  
Constant Factor ◽  
Weight Coefficients

By introducing multi-parameters, and applying weight coefficients, we prove a reverse Mulholland-type inequality in the whole plane with a best possible constant factor. Moreover, the equivalent forms and a few particular cases are 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 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.

scholarly journals On a relation to two basic Hilbert-type integral inequalities

2009 ◽  
Vol 40 (3) ◽  
pp. 217-223 ◽  
Author(s):  
Bicheng Yang
Keyword(s):  
Weight Function ◽  
Integral Inequality ◽  
Equivalent Form ◽  
Constant Factor ◽  
Integral Inequalities ◽  
Real Analysis ◽  
Best Constant ◽  
Type Integral ◽  
Best Constant Factor ◽  
Hilbert Type

In this paper, by using the way of weight function and the technic of real analysis, a new integral inequality with some parameters and a best constant factor is given, which is a relation to two basic Hilbert-type integral inequalities. The equivalent form and the reverse forms are considered.

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