{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,10]],"date-time":"2026-04-10T18:07:53Z","timestamp":1775844473831,"version":"3.50.1"},"reference-count":34,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2023,7,12]],"date-time":"2023-07-12T00:00:00Z","timestamp":1689120000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Pontificia Universidad Cat\u00f3lica del Ecuador Proyect T\u00ed- tulo","award":["UIO2022"],"award-info":[{"award-number":["UIO2022"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>In recent years, the theory of convexity has influenced every field of mathematics due to its unique characteristics. Numerous generalizations, extensions, and refinements of convexity have been introduced, and one of them is set-valued convexity. Interval-valued convex mappings are a special type of set-valued maps. These have a close relationship with symmetry analysis. One of the important aspects of the relationship between convex and symmetric analysis is the ability to work on one field and apply its principles to another. In this paper, we introduce a novel class of interval-valued (I.V.) functions called CR-\u03b3-convex functions based on a non-negative mapping \u03b3 and center-radius ordering relation. Due to its generic property, a set of new and known forms of convexity can be obtained. First, we derive new generalized discrete and integral forms of Jensen\u2019s inequalities using CR-\u03b3-convex I.V. functions. We employ this definition and Riemann-Liouville fractional operators to develop new fractional versions of Hermite-Hadamard\u2019s, Hermite-Hadamard-Fejer, and Pachpatte\u2019s type integral inequalities. We examine various key properties of this class of functions by considering them as special cases. Finally, we support our findings with interesting examples and graphical representations.<\/jats:p>","DOI":"10.3390\/sym15071405","type":"journal-article","created":{"date-parts":[[2023,7,13]],"date-time":"2023-07-13T01:43:22Z","timestamp":1689212602000},"page":"1405","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":18,"title":["I.V-CR-\u03b3-Convex Functions and Their Application in Fractional Hermite\u2013Hadamard Inequalities"],"prefix":"10.3390","volume":"15","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1567-0264","authenticated-orcid":false,"given":"Miguel","family":"Vivas-Cortez","sequence":"first","affiliation":[{"name":"Escuela de Ciencias F\u00edsicas y Matem\u00e1ticas, Facultad de Ciencias Exactas y Naturales, Pontificia Universidad Cat\u00f3lica del Ecuador, Av. 12 de Octubre 1076, Apartado, Quito 17-01-2184, Ecuador"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Sofia","family":"Ramzan","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Government College University, Faisalabad 38000, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1019-9485","authenticated-orcid":false,"given":"Muhammad Uzair","family":"Awan","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Government College University, Faisalabad 38000, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5212-6252","authenticated-orcid":false,"given":"Muhammad Zakria","family":"Javed","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Government College University, Faisalabad 38000, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Awais Gul","family":"Khan","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Government College University, Faisalabad 38000, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6105-2435","authenticated-orcid":false,"given":"Muhammad Aslam","family":"Noor","sequence":"additional","affiliation":[{"name":"Department of Mathematics, COMSATS University Islamabad, Islamabad 45550, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,7,12]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"229","DOI":"10.1007\/BF02189414","article-title":"Hermite and convexity","volume":"28","year":"1985","journal-title":"Aequationes Math."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"323","DOI":"10.4067\/S0716-09172015000400002","article-title":"Inequalities of Hermite-Hadamard type for h-convex functions on linear spaces","volume":"34","author":"Dragomir","year":"2015","journal-title":"Proyecciones"},{"key":"ref_3","first-page":"26","article-title":"Hadamard-type inequalities for s-convex functions","volume":"193","author":"Kirmaci","year":"2007","journal-title":"Appl. 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