A Half-Discrete Hardy–Mulholland-Type Inequality Involving One Multiple Upper Limit Function and One Partial Sum

Bicheng Yang, Shanhe Wu () and Jianquan Liao
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Bicheng Yang: Institute of Applied Mathematics, Longyan University, Longyan 364012, China
Shanhe Wu: Institute of Applied Mathematics, Longyan University, Longyan 364012, China
Jianquan Liao: School of Mathematics, Guangdong University of Education, Guangzhou 510303, China

Mathematics, 2025, vol. 13, issue 15, 1-16

Abstract: In this paper, by using the techniques of real analysis, with the help of the Euler–Maclaurin summation formula, Abel’s summation by parts formula, and the differentiation mid-value theorem, we establish a half-discrete Hardy–Mulholland-type inequality involving one multiple upper limit function and one partial sum. Based on the obtained inequality, we characterize the condition of the best possible constant factor related to several parameters. At the end of the paper, we illustrate that some new half-discrete Hardy–Mulholland-type inequalities can be deduced from the special values of the parameters. Our results enrich the current results in the study of half-discrete Hardy–Mulholland-type inequalities.

Keywords: half-discrete Hardy–Mulholland’s inequality; multiple upper limit function; partial sum; best possible constant factor (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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