A reverse extended Hardy–Hilbert’s inequality with parameters

Journal of Inequalities and Applications

卷:2023

Research

Bicheng Yang¹  Ricai Luo²  Xingshou Huang² 

[1] Department of Mathematics, Guangdong University of Education, 51003, Guangzhou, Guangdong, China;

[2] School of Mathematics and Statistics, Hechi University, 456300, Yizhou, Guangxi, P.R. China;

关键词: Weight coefficient;    Hardy–Hilbert’s inequality;    Equivalent statement;    Parameter;    Reverse;    26D15;    26D10;    47A05;   

DOI  :  10.1186/s13660-023-02967-5

 received in 2021-08-10, accepted in 2023-03-31,  发布年份 2023

来源: Springer

【 摘 要 】

In this paper, by virtue of the symmetry principle, applying the techniques of real analysis and Euler–Maclaurin summation formula, we construct proper weight coefficients and use them to establish a reverse extended Hardy–Hilbert’s inequality with multi-parameters. Then, we obtain the equivalent forms and some equivalent statements of the best possible constant factor related to several parameters. Finally, we illustrate how the obtained results can generate some new reverse Hardy–Hilbert-type inequalities.

【 授权许可】

CC BY   
© The Author(s) 2023

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