{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,7]],"date-time":"2026-05-07T05:25:57Z","timestamp":1778131557087,"version":"3.51.4"},"reference-count":14,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2022,7,24]],"date-time":"2022-07-24T00:00:00Z","timestamp":1658620800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Princess Nourah bint Abdulrahman University Researchers","award":["PNURSP2022R45"],"award-info":[{"award-number":["PNURSP2022R45"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>In this paper, we prove some new generalized inequalities of Hilbert-type on time scales nabla calculus by applying H\u00f6lder\u2019s inequality, Young\u2019s inequality, and Jensen\u2019s inequality. Symmetrical properties play an essential role in determining the correct methods to solve inequalities.<\/jats:p>","DOI":"10.3390\/sym14081512","type":"journal-article","created":{"date-parts":[[2022,7,25]],"date-time":"2022-07-25T04:52:47Z","timestamp":1658724767000},"page":"1512","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":9,"title":["Generalized Inequalities of Hilbert-Type on Time Scales Nabla Calculus"],"prefix":"10.3390","volume":"14","author":[{"given":"Mohammed","family":"Zakarya","sequence":"first","affiliation":[{"name":"Department of Mathematics, College of Science, King Khalid University, P.O. Box 9004, Abha 61413, Saudi Arabia"},{"name":"Department of Mathematics, Faculty of Science, Al-Azhar University, Assiut 71524, Egypt"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2222-7973","authenticated-orcid":false,"given":"Ghada","family":"AlNemer","sequence":"additional","affiliation":[{"name":"Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia"}]},{"given":"Ahmed I.","family":"Saied","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Science, Benha University, Benha 13511, Egypt"}]},{"given":"Roqia","family":"Butush","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of Jordan, Amman P.O. Box 11941, Jordan"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7251-9608","authenticated-orcid":false,"given":"Omar","family":"Bazighifan","sequence":"additional","affiliation":[{"name":"Section of Mathematics, International Telematic University Uninettuno, Corso Vittorio Emanuele II, 39, 00186 Rome, Italy"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6782-7908","authenticated-orcid":false,"given":"Haytham M.","family":"Rezk","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Science, Al-Azhar University, Nasr City 11884, Egypt"}]}],"member":"1968","published-online":{"date-parts":[[2022,7,24]]},"reference":[{"key":"ref_1","first-page":"1","article-title":"Bernerkungen sur theorie der beschrankten Bilinearformen mit unendlich vielen veranderlichen","volume":"140","author":"Schur","year":"1911","journal-title":"J. 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