{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T01:15:24Z","timestamp":1760231724440,"version":"build-2065373602"},"reference-count":16,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2022,9,30]],"date-time":"2022-09-30T00:00:00Z","timestamp":1664496000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Princess Nourah bint Abdulrahman University, Riyadh, Saudi Arabia"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Our work in this paper is based on the reverse H\u00f6lder-type dynamic inequalities illustrated by El-Deeb in 2018 and the reverse Hilbert-type dynamic inequalities illustrated by Rezk in 2021 and 2022. With the help of Specht\u2019s ratio, the concept of supermultiplicative functions, chain rule, and Jensen\u2019s inequality on time scales, we can establish some comprehensive and generalize a number of classical reverse Hilbert-type inequalities to a general time scale space. In time scale calculus, results are unified and extended. At the same time, the theory of time scale calculus is applied to unify discrete and continuous analysis and to combine them in one comprehensive form. This hybrid theory is also widely applied on symmetrical properties which play an essential role in determining the correct methods to solve inequalities. As a special case of our results when the supermultiplicative function represents the identity map, we obtain some results that have been recently published.<\/jats:p>","DOI":"10.3390\/sym14102043","type":"journal-article","created":{"date-parts":[[2022,10,11]],"date-time":"2022-10-11T03:32:56Z","timestamp":1665459176000},"page":"2043","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Some New Generalizations of Reverse Hilbert-Type Inequalities via Supermultiplicative Functions"],"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"}]},{"given":"Ahmed I.","family":"Saied","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Science, Benha University, Benha 13511, 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"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4312-8330","authenticated-orcid":false,"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":[[2022,9,30]]},"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). Uber einen Mittelwerthssatz. Nachr. Ges. Wiss. 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Spaces"},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"AlNemer, G., Saied, A.I., Zakarya, M., Abd El-Hamid, H.A., Bazighifan, O., and Rezk, H.M. (2021). Some new reverse Hilbert\u2019s inequalities on time scales. Symmetry, 13.","DOI":"10.3390\/sym13122431"},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Al Nemer, G., Zakarya, M., El-Hamid, H.A.A., Agarwal, P., and Rezk, H. (2020). Some Dynamic Hilbert-type inequality on time scales. Symmetry, 12.","DOI":"10.3390\/sym12091410"},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Bohner, M., and Peterson, A. (2001). Dynamic Equations on Time Scales: An Introduction with Applications, Birkh\u00e4user.","DOI":"10.1007\/978-1-4612-0201-1"},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Bohner, M., and Peterson, A. (2003). 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