A NEW MORE ACCURATE HILBERT-TYPE INEQUALITY INVOLVING ONE PARTIAL SUM

Aizhen Wang; Bicheng Yang

doi:10.11948/20240449

2027 Volume 17 Issue 1

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Aizhen Wang, Bicheng Yang. A NEW MORE ACCURATE HILBERT-TYPE INEQUALITY INVOLVING ONE PARTIAL SUM[J]. Journal of Applied Analysis & Computation, 2027, 17(1): 269-287. doi: 10.11948/20240449

Citation:

Aizhen Wang, Bicheng Yang. A NEW MORE ACCURATE HILBERT-TYPE INEQUALITY INVOLVING ONE PARTIAL SUM[J]. Journal of Applied Analysis & Computation, 2027, 17(1): 269-287. doi: 10.11948/20240449

A NEW MORE ACCURATE HILBERT-TYPE INEQUALITY INVOLVING ONE PARTIAL SUM

Aizhen Wang^1,,
Bicheng Yang^1, ,

1.
School of Mathematics, Guangdong University of Education, Guangzhou, Guangdong 510303, China

Author Bio: Email: ershinath@163.com(A. Wang)
Corresponding author: Email: bcyang818@163.com(B. Yang)

Abstract

Abstract

By using the weight coefficients, the Euler-Maclaurin summation formula and Abel summation by parts formula, a new more accurate Hilbert-type inequality with the power function as the internal variables involving one partial sum is given. The equivalent conditions of the best value related to a few parameters are obtained, and some particular inequalities are considered. We also provide the equivalent forms and the operator expressions.
- Weight coefficient /
- Euler-Maclaurin summation formula /
- Hardy-Hilbert's inequality /
- internal variable /
- parameter /
- partial sum
MSC: 26D15

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References

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