A MORE ACCURATE HALF-DISCRETE HILBERT-TYPE INEQUALITY INVOLVING ONE HIGHER-ORDER DERIVATIVE FUNCTION

Jianhua Zhong; Bicheng Yang; Qiang Chen

doi:10.11948/20210223

2022 Volume 12 Issue 1

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Jianhua Zhong, Bicheng Yang, Qiang Chen. A MORE ACCURATE HALF-DISCRETE HILBERT-TYPE INEQUALITY INVOLVING ONE HIGHER-ORDER DERIVATIVE FUNCTION[J]. Journal of Applied Analysis & Computation, 2022, 12(1): 378-391. doi: 10.11948/20210223

Citation:

Jianhua Zhong, Bicheng Yang, Qiang Chen. A MORE ACCURATE HALF-DISCRETE HILBERT-TYPE INEQUALITY INVOLVING ONE HIGHER-ORDER DERIVATIVE FUNCTION[J]. Journal of Applied Analysis & Computation, 2022, 12(1): 378-391. doi: 10.11948/20210223

A MORE ACCURATE HALF-DISCRETE HILBERT-TYPE INEQUALITY INVOLVING ONE HIGHER-ORDER DERIVATIVE FUNCTION

1.
School of Mathematics, Guangdong University of Education, Guangzhou, Guangdong 51003, China
2.
School of Computer Science, Guangdong University of Education, Guangzhou, Guangdong 51003, China

Corresponding author: Email: bcyang@gdei.edu.cn (B. C. Yang)
Fund Project: The authors were supported by National Natural Science Foundation of China (No. 61772140) and the Characteristic Innovation Project of Guangdong Provincial Colleges and Universities in 2020 (No. 2020KTSCX088)

Abstract

Abstract

By means of the weight functions, Hermite-Hadamards inequality and the techniques of real analysis, a new more accurate half-discrete Hilberttype inequality involving one higher-order derivative function is given. The equivalent conditions of the best possible constant factor related to a few parameters, the equivalent forms, several particular inequalities and the operator expressions are considered.
- Weight function /
- Hermite-Hadamards inequality /
- half-discrete Hilbert-type inequality /
- higher-order derivative function /
- parameter /
- best possible constant factor
MSC: 26D15, 26D10, 26A42

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References

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