{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,13]],"date-time":"2026-02-13T20:32:59Z","timestamp":1771014779182,"version":"3.50.1"},"reference-count":20,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2022,4,6]],"date-time":"2022-04-06T00:00:00Z","timestamp":1649203200000},"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>This manuscript develops the study of reverse Hilbert-type inequalities by applying reverse H\u00f6lder inequalities on T. We generalize the reverse inequality of Hilbert-type with power two by replacing the power with a new power \u03b2,\u03b2&gt;1. The main results are proved by using Specht\u2019s ratio, chain rule and Jensen\u2019s inequality. Our results (when T=N) are essentially new. Symmetrical properties play an essential role in determining the correct methods to solve inequalities.<\/jats:p>","DOI":"10.3390\/sym14040750","type":"journal-article","created":{"date-parts":[[2022,4,7]],"date-time":"2022-04-07T22:23:23Z","timestamp":1649370203000},"page":"750","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["Some New Generalizations of Reverse Hilbert-Type Inequalities on Time Scales"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-6782-7908","authenticated-orcid":false,"given":"Haytham M.","family":"Rezk","sequence":"first","affiliation":[{"name":"Department of Mathematics, Faculty of Science, Al-Azhar University, Nasr City 11884, 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 13518, Egypt"}]},{"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"}]},{"given":"Mohammed","family":"Zakarya","sequence":"additional","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"}]}],"member":"1968","published-online":{"date-parts":[[2022,4,6]]},"reference":[{"key":"ref_1","first-page":"45","article-title":"Note on a theorem of Hilbert concerning series of positive term","volume":"23","author":"Hardy","year":"1925","journal-title":"Proc. Lond. Math. Soc."},{"key":"ref_2","unstructured":"Hardy, G.H., Littlewood, J.E., and P\u00f3lya, G. (1934). Inequalities, Cambridge University Press. [2nd ed.]."},{"key":"ref_3","unstructured":"H\u00f6lder, O. (1889). 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