EQUIVALENT PROPERTY OF A MORE ACCURATE HALF-DISCRETE HILBERT'S INEQUALITY

Aizhen Wang; Bicheng Yang

doi:10.11948/20190153

2020 Volume 10 Issue 3

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Aizhen Wang, Bicheng Yang. EQUIVALENT PROPERTY OF A MORE ACCURATE HALF-DISCRETE HILBERT'S INEQUALITY[J]. Journal of Applied Analysis & Computation, 2020, 10(3): 920-934. doi: 10.11948/20190153

Citation:

Aizhen Wang, Bicheng Yang. EQUIVALENT PROPERTY OF A MORE ACCURATE HALF-DISCRETE HILBERT'S INEQUALITY[J]. Journal of Applied Analysis & Computation, 2020, 10(3): 920-934. doi: 10.11948/20190153

EQUIVALENT PROPERTY OF A MORE ACCURATE HALF-DISCRETE HILBERT'S INEQUALITY

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

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

Author Bio: Email: ershimath@163.com (A. Wang)
Corresponding author: Email: bcyang@gdei.edu.cn (B. Yang)
Fund Project: The authors were supported by National Natural Science Foundation (No. 61772140), and Science and Technology Planning Project Item of Guangzhou City (No. 201707010229)

Abstract

Abstract

By using the weight functions, the idea of introducing parameters, and Hermite-Hadamard's inequality, a more accurate half-discrete Hilbert's inequality with the nonhomogeneous kernel and its equivalent form are given. The equivalent statements of the best possible constant factor related to parameters, the operator expressions and some particular cases are considered. The cases of the relating homogeneous kernel are also deduced.
- Weight function /
- half-discrete Hilbert's inequality /
- equivalent statement /
- Hermite-Hadamard's inequality /
- operator expression
MSC: 26D15

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