{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T00:46:53Z","timestamp":1760230013479,"version":"build-2065373602"},"reference-count":21,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2022,7,7]],"date-time":"2022-07-07T00:00:00Z","timestamp":1657152000000},"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 important work, we discuss some novel Hilbert-type dynamic inequalities on time scales. The inequalities investigated here generalize several known dynamic inequalities on time scales and unify and extend some continuous inequalities and their corresponding discrete analogues. Our results will be proved by using some algebraic inequalities, H\u00f6lder inequality, and Jensen\u2019s inequality on time scales.<\/jats:p>","DOI":"10.3390\/sym14071395","type":"journal-article","created":{"date-parts":[[2022,7,7]],"date-time":"2022-07-07T22:11:47Z","timestamp":1657231907000},"page":"1395","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["On Some Important Class of Dynamic Hilbert\u2019s-Type Inequalities on Time Scales"],"prefix":"10.3390","volume":"14","author":[{"given":"Hassan M.","family":"El-Owaidy","sequence":"first","affiliation":[{"name":"Department of Mathematics, Faculty of Science, Al-Azhar University, Nasr City 11884, Cairo, Egypt"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2822-4092","authenticated-orcid":false,"given":"Ahmed A.","family":"El-Deeb","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Science, Al-Azhar University, Nasr City 11884, Cairo, Egypt"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Samer D.","family":"Makharesh","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Science, Al-Azhar University, Nasr City 11884, Cairo, Egypt"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0286-7244","authenticated-orcid":false,"given":"Dumitru","family":"Baleanu","sequence":"additional","affiliation":[{"name":"Institute of Space Science, 077125 Bucharest, Romania"},{"name":"Department of Mathematics, Cankaya University, 06530 Ankara, Turkey"},{"name":"Department of Medical Research, China Medical University, Taichung 40447, Taiwan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Clemente","family":"Cesarano","sequence":"additional","affiliation":[{"name":"Section of Mathematics, International Telematic University Uninettuno, Corso Vittorio Emanuele II, 39, 00186 Rome, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,7,7]]},"reference":[{"key":"ref_1","unstructured":"Hardy, G.H., Littlewood, J.E., and Polya, G. 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