An extended reverse Hardy–Hilbert’s inequality in the whole plane [PDF]
Journal of Inequalities and Applications, 2018 Using weight coefficients, a complex integral formula, and Hermite–Hadamard’s inequality, we give an extended reverse Hardy–Hilbert’s inequality in the whole plane with multiparameters and a best possible constant factor.
Qiang Chen, Bicheng Yang
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An extended Hilbert’s integral inequality in the whole plane with parameters [PDF]
Journal of Inequalities and Applications, 2018 By introducing independent parameters and interval variables, applying the weight functions and the technique of real analysis, an extended Hilbert’s integral inequality in the whole plane with parameters and a best possible constant factor is provided ...
Leping He, Yin Li, Bicheng Yang
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Equivalent property of a half-discrete Hilbert’s inequality with parameters [PDF]
Journal of Inequalities and Applications, 2018 By using the weight functions and the idea of introducing parameters, a half-discrete Hilbert inequality with a nonhomogeneous kernel and its equivalent form are given.
Zhenxiao Huang, Bicheng Yang
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A Reverse Hardy–Hilbert’s Inequality Containing Multiple Parameters and One Partial Sum
Mathematics, 2022 In this work, by introducing multiple parameters and utilizing the Euler–Maclaurin summation formula and Abel’s partial summation formula, we first establish a reverse Hardy–Hilbert’s inequality containing one partial sum as the terms of double series ...
Bicheng Yang, Shanhe Wu, Xingshou Huang
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A New Extension of Hardy-Hilbert’s Inequality Containing Kernel of Double Power Functions
Mathematics, 2020 In this paper, we provide a new extension of Hardy-Hilbert’s inequality with the kernel consisting of double power functions and derive its equivalent forms.
Bicheng Yang, Shanhe Wu, Qiang Chen
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Hilbert’s Double Series Theorem’s Extensions via the Mathieu Series Approach
Axioms, 2022 The author’s research devoted to the Hilbert’s double series theorem and its various further extensions are the focus of a recent survey article.
Tibor K. Pogány
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A New Reverse Extended Hardy–Hilbert’s Inequality with Two Partial Sums and Parameters
Axioms, 2023 By using the methods of real analysis and the mid-value theorem, we introduce some lemmas and obtain a new reverse extended Hardy–Hilbert’s inequality with two partial sums and multi-parameters.
Jianquan Liao, Bicheng Yang
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On New Extensions of Hilbert's Integral Inequality
International Journal of Mathematics and Mathematical Sciences, 2008 It is shown that some new extensions of Hilbert's integral inequality with parameter λ(λ>1/2) can be established by introducing a proper weight function. In particular, when λ=1, a refinement of Hilbert's integral inequality is obtained. As applications,
He Leping, Gao Mingzhe, Zhou Yu
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A Generalization on Some New Types of Hardy-Hilbert’s Integral Inequalities
Journal of Function Spaces and Applications, 2013 Sulaiman presented, in 2008, new kinds of Hardy-Hilbert’s integral inequality in which the weight function is homogeneous. In this paper, we present a generalization on the kinds of Hardy-Hilbert’s integral inequality.
Banyat Sroysang
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On Some Extensions of Hardy-Hilbert's Inequality and Applications
Journal of Inequalities and Applications, 2008 By introducing some parameters we establish an extension of Hardy-Hilbert's integral inequality and the corresponding inequality for series. As an application, the reverses, some particular results and their equivalent forms are considered.
Laith Emil Azar
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