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Open AccessArticle
A Half-Discrete Hardy–Mulholland-Type Inequality Involving One Multiple Upper Limit Function and One Partial Sum
by
Bicheng Yang
Bicheng Yang 1,2,
Shanhe Wu
Shanhe Wu 1,*
and
Jianquan Liao
Jianquan Liao 2
1
Institute of Applied Mathematics, Longyan University, Longyan 364012, China
2
School of Mathematics, Guangdong University of Education, Guangzhou 510303, China
*
Author to whom correspondence should be addressed.
Mathematics 2025, 13(15), 2497; https://doi.org/10.3390/math13152497 (registering DOI)
Submission received: 5 July 2025
/
Revised: 31 July 2025
/
Accepted: 1 August 2025
/
Published: 3 August 2025
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.
Share and Cite
MDPI and ACS Style
Yang, B.; Wu, S.; Liao, J.
A Half-Discrete Hardy–Mulholland-Type Inequality Involving One Multiple Upper Limit Function and One Partial Sum. Mathematics 2025, 13, 2497.
https://doi.org/10.3390/math13152497
AMA Style
Yang B, Wu S, Liao J.
A Half-Discrete Hardy–Mulholland-Type Inequality Involving One Multiple Upper Limit Function and One Partial Sum. Mathematics. 2025; 13(15):2497.
https://doi.org/10.3390/math13152497
Chicago/Turabian Style
Yang, Bicheng, Shanhe Wu, and Jianquan Liao.
2025. "A Half-Discrete Hardy–Mulholland-Type Inequality Involving One Multiple Upper Limit Function and One Partial Sum" Mathematics 13, no. 15: 2497.
https://doi.org/10.3390/math13152497
APA Style
Yang, B., Wu, S., & Liao, J.
(2025). A Half-Discrete Hardy–Mulholland-Type Inequality Involving One Multiple Upper Limit Function and One Partial Sum. Mathematics, 13(15), 2497.
https://doi.org/10.3390/math13152497
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