{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T00:55:55Z","timestamp":1760230555583,"version":"build-2065373602"},"reference-count":35,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2022,7,26]],"date-time":"2022-07-26T00:00:00Z","timestamp":1658793600000},"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 paper, firstly, we present an integral identity for functions of two variables via Riemann\u2013Liouville fractional integrals. Then, a Newton-type inequality via partially differentiable coordinated convex mappings is derived by taking the absolute value of the obtained identity. Moreover, several inequalities are obtained with the aid of the H\u00f6lder and power mean inequality. In addition, we investigate some Newton-type inequalities utilizing mappings of two variables with bounded variation. Finally, we gave some mathematical examples and their graphical behavior to validate the obtained inequalities.<\/jats:p>","DOI":"10.3390\/sym14081526","type":"journal-article","created":{"date-parts":[[2022,7,29]],"date-time":"2022-07-29T01:41:16Z","timestamp":1659058876000},"page":"1526","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["On Fractional Newton Inequalities via Coordinated Convex Functions"],"prefix":"10.3390","volume":"14","author":[{"given":"P\u0131nar","family":"K\u00f6sem","sequence":"first","affiliation":[{"name":"Department of Mathematics, Faculty of Science and Arts, D\u00fczce University, D\u00fczce 81620, Turkey"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2075-944X","authenticated-orcid":false,"given":"Hasan","family":"Kara","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Science and Arts, D\u00fczce University, D\u00fczce 81620, Turkey"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8843-955X","authenticated-orcid":false,"given":"H\u00fcseyin","family":"Budak","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Science and Arts, D\u00fczce University, D\u00fczce 81620, Turkey"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5341-4926","authenticated-orcid":false,"given":"Muhammad Aamir","family":"Ali","sequence":"additional","affiliation":[{"name":"Jiangsu Key Laboratory of NSLSCS, School of Mathematical Sciences, Nanjing Normal University, Nanjing 210023, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7469-5402","authenticated-orcid":false,"given":"Kamsing","family":"Nonlaopon","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen 40002, Thailand"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,7,26]]},"reference":[{"key":"ref_1","first-page":"533","article-title":"On Simpson\u2019s inequality and applications","volume":"5","author":"Dragomir","year":"2000","journal-title":"J. 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