On an extended Hardy-Littlewood-Polya’s inequality

Bicheng Yang; Shanhe Wu; Qiang Chen; Bicheng Yang; Shanhe Wu; Qiang Chen

doi:10.3934/math.2020106

AIMS Mathematics

2020, Volume 5, Issue 2: 1550-1561. doi: 10.3934/math.2020106

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Research article

On an extended Hardy-Littlewood-Polya’s inequality

1.
Institute of Applied Mathematics, Longyan University, Longyan, Fujian 364012, China
2.
Department of Mathematics, Longyan University, Longyan, Fujian 364012, China
3.
Department of Computer Science, Guangdong University of Education, Guangzhou, Guangdong 510303, China

Received: 27 October 2019 Accepted: 10 January 2020 Published: 03 February 2020
MSC : 26D15, 26D10, 26A42

By utilization of the weight coefficients, the idea of introducing parameters and Euler-Maclaurin summation formula, an extended Hardy-Littlewood-Polya's inequality and its equivalent form are established. The equivalent statements of the best possible constant factor involving several parameters, and some particular cases are provided. The operator expressions of the obtained results are also considered.
- weight coefficient,
- Hardy-Littlewood-Polya’s inequality,
- Euler-Maclaurin summation formula,
- equivalent statement,
- parameter
Citation: Bicheng Yang, Shanhe Wu, Qiang Chen. On an extended Hardy-Littlewood-Polya’s inequality[J]. AIMS Mathematics, 2020, 5(2): 1550-1561. doi: 10.3934/math.2020106

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Abstract

By utilization of the weight coefficients, the idea of introducing parameters and Euler-Maclaurin summation formula, an extended Hardy-Littlewood-Polya's inequality and its equivalent form are established. The equivalent statements of the best possible constant factor involving several parameters, and some particular cases are provided. The operator expressions of the obtained results are also considered.

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