ON A NEW HALF-DISCRETE HILBERT-TYPE INEQUALITY WITH THE MULTIPLE UPPER LIMIT FUNCTION AND THE PARTIAL SUMS

Aizhen Wang; Hong Yong; Bicheng Yang

doi:10.11948/20210423

2022 Volume 12 Issue 2

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Aizhen Wang, Hong Yong, Bicheng Yang. ON A NEW HALF-DISCRETE HILBERT-TYPE INEQUALITY WITH THE MULTIPLE UPPER LIMIT FUNCTION AND THE PARTIAL SUMS[J]. Journal of Applied Analysis & Computation, 2022, 12(2): 814-830. doi: 10.11948/20210423

Citation:

Aizhen Wang, Hong Yong, Bicheng Yang. ON A NEW HALF-DISCRETE HILBERT-TYPE INEQUALITY WITH THE MULTIPLE UPPER LIMIT FUNCTION AND THE PARTIAL SUMS[J]. Journal of Applied Analysis & Computation, 2022, 12(2): 814-830. doi: 10.11948/20210423

ON A NEW HALF-DISCRETE HILBERT-TYPE INEQUALITY WITH THE MULTIPLE UPPER LIMIT FUNCTION AND THE PARTIAL SUMS

1.
School of Mathematics, Guangdong University of Education, Guangzhou, Guangdong 510303, China
2.
Department of Applied Mathematics, Guangzhou Huashang College, Guangdong, Guangzhou 511300, China

Corresponding author: Email: mathhongyong@163.com(H. Yong)
Fund Project: The authors were supported by the National Natural Science Foundation of China (No. 61772040), the Characteristic Innovation Project of Guangdong Provincial Colleges and Universities in 2020 (No. 2020KTSCX088)

Abstract

Abstract

By means of the weight coefficients, the Euler-Maclaurin summation formula and Abel's summation by parts formula, a new half-discrete Hilbert-type inequality with the power function as the interval variables as well as one multiple upper limit function and one partial sums is given. As applications, the equivalent conditions of the best possible constant factor in a particular inequality related to a few parameters and some particular cases are considered. We also obtain the equivalent forms and the operator expression in the case of m=0.
- Weight coefficient /
- Euler-Maclaurin summation formula /
- Half-dis-crete Hilbert-type inequality /
- parameter /
- partial sums /
- multiple upper limit function
MSC: 26D15

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