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Keywords = half-discrete multidimensional Hilbert-type inequality

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13 pages, 290 KB  
Article
A More Accurate Half-Discrete Multidimensional Hilbert-Type Inequality Involving One Multiple Upper Limit Function
by Yong Hong, Yanru Zhong and Bicheng Yang
Axioms 2023, 12(2), 211; https://doi.org/10.3390/axioms12020211 - 16 Feb 2023
Cited by 4 | Viewed by 1602
Abstract
By means of the weight functions, the idea of introduced parameters, using the transfer formula and Hermite–Hadamard’s inequality, a more accurate half-discrete multidimensional Hilbert-type inequality with the homogeneous kernel as [...] Read more.
By means of the weight functions, the idea of introduced parameters, using the transfer formula and Hermite–Hadamard’s inequality, a more accurate half-discrete multidimensional Hilbert-type inequality with the homogeneous kernel as 1(x+||kξ||α)λ(x,λ>0) involving one multiple upper limit function is given, which is a new application of Hilbert-type inequalities. The equivalent conditions of the best possible constant factor related to several parameters are considered. The equivalent forms the operator expressions and some particular inequalities are obtained. Full article
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