A NEW MULTIDIMENSIONAL HILBERT-TYPE INEQUALITY WITH TWO INTERNAL VARIABLES INVOLVING ONE PARTIAL SUM

Ling Peng; Bicheng Yang

doi:10.11948/20240257

2026 Volume 16 Issue 3

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Ling Peng, Bicheng Yang. A NEW MULTIDIMENSIONAL HILBERT-TYPE INEQUALITY WITH TWO INTERNAL VARIABLES INVOLVING ONE PARTIAL SUM[J]. Journal of Applied Analysis & Computation, 2026, 16(3): 1573-1593. doi: 10.11948/20240257

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Ling Peng, Bicheng Yang. A NEW MULTIDIMENSIONAL HILBERT-TYPE INEQUALITY WITH TWO INTERNAL VARIABLES INVOLVING ONE PARTIAL SUM[J]. Journal of Applied Analysis & Computation, 2026, 16(3): 1573-1593. doi: 10.11948/20240257

A NEW MULTIDIMENSIONAL HILBERT-TYPE INEQUALITY WITH TWO INTERNAL VARIABLES INVOLVING ONE PARTIAL SUM

Ling Peng^1,,
Bicheng Yang^2, ,

1.
School of Medical Humanity and Information Management, Hunan University of Medicine, Huaihua, Hunan 418000, China
2.
School of Mathematics, Guangdong University of Education, Guangzhou, Guangdong 510303, China

Author Bio: Email: huangxianyong@gdei.edu.cn(L. Peng)
Corresponding author: Email: bcyang818@163.com(B. Yang)

Abstract

Abstract

This study explores a new multidimensional Hilbert-type inequality involving one partial sum, by utilizing transfer formula and Hermite-Hadamard's inequality. The kernel $ \frac{1}{\left(u(m)+\left\Vert v(k)\right\Vert_{\alpha}\right)^{\lambda }}(\lambda >0) $ in the new inequality has two general internal variables compared with previous work, and the best value is achieved with certain parameters. Finally, the equivalent forms, the operator expressions and some particular cases are presented.
- Multidimensional Hilbert-type inequality /
- weight function /
- best value /
- parameter /
- partial sum
MSC: 26D15

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References

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