{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T03:03:14Z","timestamp":1760151794378,"version":"build-2065373602"},"reference-count":30,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2022,4,12]],"date-time":"2022-04-12T00:00:00Z","timestamp":1649721600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>In this paper, Hardy\u2013Leindler, Hardy\u2013Yang and Hwang type inequalities are extended on time scales calculus. These extensions are depending upon use of symmetric multiple delta integrals. The target is achieved by utilizing some inequalities in literature along with mathematical induction principle and Fubini\u2019s theorem on time scales. The obtained inequalities are discussed in discrete, continuous and quantum calculus in search of applications. Particular cases of proved results include Hardy, Copson, Hardy\u2013Littlewood, Levinson and Bennett-type inequalities for symmetric sums.<\/jats:p>","DOI":"10.3390\/sym14040802","type":"journal-article","created":{"date-parts":[[2022,4,12]],"date-time":"2022-04-12T22:48:45Z","timestamp":1649803725000},"page":"802","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Hardy\u2013Leindler, Yang and Hwang Inequalities for Functions of Several Variables via Time Scale Calculus"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1627-4503","authenticated-orcid":false,"given":"Ammara","family":"Nosheen","sequence":"first","affiliation":[{"name":"Department of Mathematics, University of Sargodha, Sargodha 40100, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Huma","family":"Akbar","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics, The University of Lahore, Sargodha Campus, Sargodha 40100, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Maroof Ahmad","family":"Sultan","sequence":"additional","affiliation":[{"name":"Nusrat Jahan College Chenab Nagar, Chiniot 35400, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0862-0648","authenticated-orcid":false,"given":"Jae Dong","family":"Chung","sequence":"additional","affiliation":[{"name":"Department of Mechanical Engineering, Sejong University, Seoul 05006, Korea"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1949-5643","authenticated-orcid":false,"given":"Nehad Ali","family":"Shah","sequence":"additional","affiliation":[{"name":"Department of Mechanical Engineering, Sejong University, Seoul 05006, Korea"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,4,12]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"314","DOI":"10.1007\/BF01199965","article-title":"Note on a theorem of Hilbert","volume":"6","author":"Hardy","year":"1920","journal-title":"Math. 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