{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,13]],"date-time":"2026-02-13T20:32:15Z","timestamp":1771014735668,"version":"3.50.1"},"reference-count":20,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2021,12,15]],"date-time":"2021-12-15T00:00:00Z","timestamp":1639526400000},"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 paper is interested in establishing some new reverse Hilbert-type inequalities, by using chain rule on time scales, reverse Jensen\u2019s, and reverse H\u00f6lder\u2019s with Specht\u2019s ratio and mean inequalities. To get the results, we used the Specht\u2019s ratio function and its applications for reverse inequalities of Hilbert-type. Symmetrical properties play an essential role in determining the correct methods to solve inequalities. The new inequalities in special cases yield some recent relevance, which also provide new estimates on inequalities of these type.<\/jats:p>","DOI":"10.3390\/sym13122431","type":"journal-article","created":{"date-parts":[[2021,12,15]],"date-time":"2021-12-15T21:47:36Z","timestamp":1639604856000},"page":"2431","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":16,"title":["Some New Reverse Hilbert\u2019s Inequalities on Time Scales"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2222-7973","authenticated-orcid":false,"given":"Ghada","family":"AlNemer","sequence":"first","affiliation":[{"name":"Department of Mathematical Science, College of Science, Princess Nourah Bint Abdulrahman University, P.O. Box 105862, Riyadh 11656, Saudi Arabia"}]},{"given":"Ahmed I.","family":"Saied","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Science, Benha University, Benha 13511, Egypt"}]},{"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"}]},{"given":"Hoda A.","family":"Abd El-Hamid","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Computer Science, Faculty of Science, Beni-Suef University, Beni-Suef 62511, 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"},{"name":"Department of Mathematics, Faculty of Science, Hadhramout University, Hadhramout 50512, Yemen"}]},{"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":[[2021,12,15]]},"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. 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