scholarly journals Two new forms of Hilbert integral inequality

2014 ◽  
pp. 937-946 ◽  
Author(s):  
Laith E. Azar
Keyword(s):  
Integral Inequality ◽  
Hilbert Integral

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 A Hilbert Integral-Type Inequality with Parameters

2010 ◽  
Vol 2010 ◽  
pp. 1-11
Author(s):  
Shang Xiaozhou ◽  
Gao Mingzhe
Keyword(s):  
Kernel Function ◽  
Integral Inequality ◽  
Type Inequality ◽  
Constant Factor ◽  
Integral Type ◽  
Type Integral ◽  
Hilbert Type ◽  
Hilbert Integral

A Hilbert-type integral inequality with parametersαand(α,λ>0)can be established by introducing a nonhomogeneous kernel function. And the constant factor is proved to be the best possible. And then some important and especial results are enumerated. As applications, some equivalent forms are studied.

scholarly journals A new form of Hilbert integral inequality

2018 ◽  
pp. 379-390
Author(s):  
Tserendorj Batbold ◽  
Laith E. Azar
Keyword(s):  
Integral Inequality ◽  
New Form ◽  
Hilbert Integral

scholarly journals On new generalizations of the Hilbert integral inequality

2007 ◽  
Vol 326 (2) ◽  
pp. 1452-1457 ◽  
Author(s):  
Zhongxue Lü ◽  
Mingzhe Gao ◽  
Lokenath Debnath
Keyword(s):  
Integral Inequality ◽  
Hilbert Integral

scholarly journals Some generalizations of the Hermite–Hadamard integral inequality

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Slavko Simić ◽  
Bandar Bin-Mohsin
Keyword(s):  
Integral Inequality ◽  
Target Function ◽  
Convexity Property ◽  
Concave Functions ◽  
Differentiable Functions

AbstractIn this article we give two possible generalizations of the Hermite–Hadamard integral inequality for the class of twice differentiable functions, where the convexity property of the target function is not assumed in advance. They represent a refinement of this inequality in the case of convex/concave functions with numerous applications.

scholarly journals A new generalization of some quantum integral inequalities for quantum differentiable convex functions

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Yi-Xia Li ◽  
Muhammad Aamir Ali ◽  
Hüseyin Budak ◽  
Mujahid Abbas ◽  
Yu-Ming Chu
Keyword(s):  
Integral Inequality ◽  
Convex Functions ◽  
Integral Identity ◽  
Integral Inequalities ◽  
Quantum Integral ◽  
Special Cases

AbstractIn this paper, we offer a new quantum integral identity, the result is then used to obtain some new estimates of Hermite–Hadamard inequalities for quantum integrals. The results presented in this paper are generalizations of the comparable results in the literature on Hermite–Hadamard inequalities. Several inequalities, such as the midpoint-like integral inequality, the Simpson-like integral inequality, the averaged midpoint–trapezoid-like integral inequality, and the trapezoid-like integral inequality, are obtained as special cases of our main results.

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