{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,20]],"date-time":"2026-04-20T05:55:48Z","timestamp":1776664548700,"version":"3.51.2"},"reference-count":28,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2022,4,2]],"date-time":"2022-04-02T00:00:00Z","timestamp":1648857600000},"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>There is a strong correlation between convexity and symmetry concepts. In this study, we investigated the new generic class of functions called the (n,m)\u2013generalized convex and studied its basic algebraic properties. The Hermite\u2013Hadamard inequality for the (n,m)\u2013generalized convex function, for the products of two functions and of this type, were proven. Moreover, this class of functions was applied to several known identities; midpoint-type inequalities of Ostrowski and Simpson were derived. Our results are extensions of many previous contributions related to integral inequalities via different convexities.<\/jats:p>","DOI":"10.3390\/sym14040722","type":"journal-article","created":{"date-parts":[[2022,4,3]],"date-time":"2022-04-03T06:04:01Z","timestamp":1648965841000},"page":"722","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":11,"title":["New Generalized Class of Convex Functions and Some Related Integral Inequalities"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-0115-3079","authenticated-orcid":false,"given":"Artion","family":"Kashuri","sequence":"first","affiliation":[{"name":"Department of Mathematics, Faculty of Technical Science, University \u201cIsmail Qemali\u201d, 9400 Vlora, Albania"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0634-2370","authenticated-orcid":false,"given":"Ravi P.","family":"Agarwal","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Texas A & M University-Kingsville, Kingsville, TX 78363, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6837-8075","authenticated-orcid":false,"given":"Pshtiwan Othman","family":"Mohammed","sequence":"additional","affiliation":[{"name":"Department of Mathematics, College of Education, University of Sulaimani, Sulaimani 46001, Kurdistan Region, Iraq"}],"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"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2908-1807","authenticated-orcid":false,"given":"Khadijah M.","family":"Abualnaja","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics, College of Science, Taif University, P.O. Box 11099, Taif 21944, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0365-0282","authenticated-orcid":false,"given":"Yasser S.","family":"Hamed","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics, College of Science, Taif University, P.O. Box 11099, Taif 21944, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,4,2]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Kashuri, A., Meftah, B., Mohammed, P.O., Lupa\u015f, A.A., Abdalla, B., Hamed, Y.S., and Abdeljawad, T. (2021). Fractional weighted Ostrowski-type inequalities and their applications. 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