Equivalent Conditions of a Hilbert-Type Multiple Integral Inequality Holding by Jianquan Liao, Yong Hong, Bicheng Yang

“…Let ∑i=1n1/pi=1pi>1, in this paper, by using the method of weight functions and technique of real analysis; it is proved that the equivalent parameter condition for the validity of multiple integral Hilbert-type inequality ∫R+nKx1,⋯,xn∏i=1nfixi dx1⋯dxn≤M∏i=1nfipi,αi with homogeneous kernel Kx1,⋯,xn of order λ is ∑i=1nαi/pi=λ+n−1, and the calculation formula of its optimal constant factor is obtained. The basic theory and method of constructing a Hilbert-type multiple integral inequality with the homogeneous kernel and optimal constant factor are solved.…”
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On a More Accurate Half-Discrete Mulholland-Type Inequality Involving One Multiple Upper Limit Function by Xianyong Huang, Bicheng Yang

“…The equivalent conditions of the best possible constant factor related to multiparameters are studied. …”
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A Multiparameter Hardy–Hilbert-Type Inequality Containing Partial Sums as the Terms of Series by Jianquan Liao, Shanhe Wu, Bicheng Yang

“…Based on the obtained inequality, we discuss the equivalent statements of the best possible constant factor related to several parameters. Moreover, we illustrate how the inequality obtained can generate some new Hardy–Hilbert-type inequalities.…”
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A Hilbert Integral-Type Inequality with Parameters by Shang Xiaozhou, Gao Mingzhe

“…A Hilbert-type integral inequality with parameters α and (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. …”
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A Hilbert-Type Integral Inequality with Multiparameters and a Nonhomogeneous Kernel by Qiong Liu, Wenbing Sun

“…We first introduce Γ-function and Riemann ζ-function to characterize the constant factor jointly. A Hilbert-type integral inequality with multiparameters and a nonhomogeneous kernel is given using the way of weight function and the technique of real analysis. …”
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Equivalent Property of a Hilbert-Type Integral Inequality Related to the Beta Function in the Whole Plane by Dongmei Xin, Bicheng Yang, Aizhen Wang

“…By means of the technique of real analysis and the weight functions, a few equivalent statements of a Hilbert-type integral inequality with the nonhomogeneous kernel in the whole plane are obtained. The constant factor related to the beta function is proved to be the best possible. …”
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Some Results on Equivalence Groups by J. C. Ndogmo

“…In addition, the Levidecomposition of the Lie algebra associated with the larger group is found; the Levi factor of which is shown to be equal, up to a constant factor, to the Lie algebra associated with the smaller group.…”
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On a Parametric Mulholland-Type Inequality and Applications by Bicheng Yang, Meifa Huang, Yanru Zhong

“…The equivalent statements of the best possible constant factor related to a few parameters are provided. …”
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On a New Extension of Mulholland’s Inequality in the Whole Plane by Bicheng Yang, Yanru Zhong, Qiang Chen

“…A new, more accurate extension of Mulholland’s inequality in the whole plane with a best possible constant factor is presented by introducing independent parameters, applying weight coefficients and using Hermite-Hadamard’s inequality. …”
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Scalable Video Streaming for Single-Hop Wireless Networks Using a Contention-Based Access MAC Protocol by Monchai Lertsutthiwong, Thinh Nguyen, Alan Fern

“…Consequently, we present a more expensive heuristic algorithm that guarantees to approximate the optimal solution within a constant factor. Simulation results demonstrate that our proposed framework can improve the video quality up to 26% as compared to those of the existing approaches.…”
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L’utilisation du bois dans les aménagements portuaires antiques de Narbonne/Narbo Martius (Aude) by Corinne Sanchez, Jean-Michel Fabre, Sophie Coadic, Julie Labussière, Benoit Favennec, Marie-Pierre Jézégou, Stéphanie Wicha

“…The principle of aligning piles, planks and caissons is a constant factor –although with variants– in the construction and maintenance of these dykes over several centuries. …”
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Generalizations of Hardy's integral inequalities by Yang Bicheng, Lokenath Debnath

“…Some cases concerning whether the constant factors involved in these inequalities are best possible are discussed in some detail.…”
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Parameterized Hilbert-Type Integral Inequalities in the Whole Plane by Qiliang Huang, Shanhe Wu, Bicheng Yang

“…By the use of the way of real analysis, we estimate the weight functions and give some new Hilbert-type integral inequalities in the whole plane with nonhomogeneous kernels and multiparameters. The constant factors related to the hypergeometric function and the beta function are proved to be the best possible. …”
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Some New Refined General Boas-Type Inequalities by A. Čižmešija, J. Pečarić, D. Pokaz

“…As a consequence of the result obtained, we derive a new class of Hardy- and Pólya-Knopp-type inequalities related to balls in ℝn and prove that constant factors involved in their right-hand sides are the best possible.…”
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Recent Developments of Hilbert-Type Discrete and Integral Inequalities with Applications by Lokenath Debnath, Bicheng Yang

“…Special attention is given to many equivalent inequalities and to conditions under which the constant factors involved in inequalities are the best possible. …”
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