{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,4]],"date-time":"2025-12-04T14:46:06Z","timestamp":1764859566669,"version":"build-2065373602"},"reference-count":15,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2023,6,12]],"date-time":"2023-06-12T00:00:00Z","timestamp":1686528000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Deanship of Scientific Research at King Khalid University","award":["RGP 2\/414\/44"],"award-info":[{"award-number":["RGP 2\/414\/44"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Through the paper, we present several inequalities involving C-monotonic functions with C\u22651, on nabla calculus via time scales. It is known that dynamic inequalities generate many different inequalities in different calculus. The main results will be proved by applying the chain rule formula on nabla calculus. As a special case for our results, when T=R, we obtain the continuous analouges of inequalities that had previously been proved in the literature. When T=N, the results, to the best of the authors\u2019 knowledge, are essentially new. Symmetrical properties of C-monotonic functions are critical in determining the best way to solve inequalities.<\/jats:p>","DOI":"10.3390\/sym15061248","type":"journal-article","created":{"date-parts":[[2023,6,13]],"date-time":"2023-06-13T01:35:30Z","timestamp":1686620130000},"page":"1248","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Novel Integral Inequalities on Nabla Time Scales with C-Monotonic Functions"],"prefix":"10.3390","volume":"15","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-4312-8330","authenticated-orcid":false,"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"}]},{"given":"A. I.","family":"Saied","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Science, Benha University, Benha 13511, Egypt"}]},{"given":"Maha","family":"Ali","sequence":"additional","affiliation":[{"name":"Department of Mathematics, College of Arts and Sciences, Sarat Abidah, King Khalid University, P.O. Box 64512, Abha 62529, Saudi Arabia"}]},{"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, Cairo 11884, Egypt"}]},{"given":"Mohammed R.","family":"Kenawy","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Science, Fayoum University, Fayoum 63514, Egypt"}]}],"member":"1968","published-online":{"date-parts":[[2023,6,12]]},"reference":[{"key":"ref_1","first-page":"133","article-title":"Weighted inequalities for monotone and concave functions","volume":"116","author":"Heinig","year":"1995","journal-title":"Stud. Math."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"235","DOI":"10.1006\/jmaa.1997.5646","article-title":"Integral inequalities for monotone functions","volume":"215","author":"Persson","year":"1997","journal-title":"J. Math. Anal. 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