{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T02:28:20Z","timestamp":1760149700788,"version":"build-2065373602"},"reference-count":30,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2023,9,10]],"date-time":"2023-09-10T00:00:00Z","timestamp":1694304000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Science Foundation of China","award":["61772140","2022GXJK290"],"award-info":[{"award-number":["61772140","2022GXJK290"]}]},{"name":"2022 Guangdong Provincial Education Science Planning Project (Higher Education Project)","award":["61772140","2022GXJK290"],"award-info":[{"award-number":["61772140","2022GXJK290"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>By the use of the techniques of analysis and some useful formulas, we give a new extension of Hilbert-type inequality with two internal variables involving one partial sums, which is a refinement of a published inequality. We provide a few equivalent conditions of the best possible constant related to multi parameters. We obtain the equivalent inequalities, the operator expressions as well as a few inequalities with the particular parameters as applications.<\/jats:p>","DOI":"10.3390\/axioms12090871","type":"journal-article","created":{"date-parts":[[2023,9,11]],"date-time":"2023-09-11T10:42:49Z","timestamp":1694428969000},"page":"871","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["An Extended Hilbert-Type Inequality with Two Internal Variables Involving One Partial Sums"],"prefix":"10.3390","volume":"12","author":[{"given":"Aizhen","family":"Wang","sequence":"first","affiliation":[{"name":"School of Mathematics, Guangdong University of Education, Guangzhou 510303, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Bicheng","family":"Yang","sequence":"additional","affiliation":[{"name":"School of Mathematics, Guangdong University of Education, Guangzhou 510303, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,9,10]]},"reference":[{"key":"ref_1","unstructured":"Hardy, G.H., Littlewood, J.E., and Polya, G. 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