{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T02:17:32Z","timestamp":1760235452800,"version":"build-2065373602"},"reference-count":18,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2021,8,23]],"date-time":"2021-08-23T00:00:00Z","timestamp":1629676800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["No. 61772140"],"award-info":[{"award-number":["No. 61772140"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>In this paper, by virtue of the symmetry principle, we construct proper weight coefficients and use them to establish a more accurate half-discrete Hilbert-type inequality involving one upper limit function and one partial sum. Then, we prove the new inequality with the help of the Euler\u2013Maclaurin summation formula and Abel\u2019s partial summation formula. Finally, we illustrate how the obtained results can generate some new half-discrete Hilbert-type inequalities.<\/jats:p>","DOI":"10.3390\/sym13081548","type":"journal-article","created":{"date-parts":[[2021,8,23]],"date-time":"2021-08-23T23:19:33Z","timestamp":1629760773000},"page":"1548","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["A More Accurate Half-Discrete Hilbert-Type Inequality Involving One upper Limit Function and One Partial Sum"],"prefix":"10.3390","volume":"13","author":[{"given":"Xianyong","family":"Huang","sequence":"first","affiliation":[{"name":"Department of Mathematics, Guangdong University of Education, Guangzhou 510303, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7413-6563","authenticated-orcid":false,"given":"Shanhe","family":"Wu","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Longyan University, Longyan 364012, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Bicheng","family":"Yang","sequence":"additional","affiliation":[{"name":"Institute of Applied Mathematics, Longyan University, Longyan 364012, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,8,23]]},"reference":[{"key":"ref_1","unstructured":"Hardy, G.H., Littlewood, J.E., and Polya, G. 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