{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T03:21:26Z","timestamp":1760239286532,"version":"build-2065373602"},"reference-count":38,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2020,10,15]],"date-time":"2020-10-15T00:00:00Z","timestamp":1602720000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>In this paper, the authors analyse and study some recent publications about integral inequalities related to generalized convex functions of several variables and the use of extended fractional integrals. In particular, they establish a new Hermite\u2013Hadamard inequality for generalized coordinate \u03d5-convex functions via an extension of the Riemann\u2013Liouville fractional integral. Furthermore, an interesting identity for functions with two variables is obtained, and with the use of it, some new extensions of trapezium-type inequalities using Raina\u2019s special function via generalized coordinate \u03d5-convex functions are developed. Various special cases have been studied. At the end, a brief conclusion is given as well.<\/jats:p>","DOI":"10.3390\/axioms9040117","type":"journal-article","created":{"date-parts":[[2020,10,15]],"date-time":"2020-10-15T09:02:03Z","timestamp":1602752523000},"page":"117","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Trapezium-Type Inequalities for an Extension of Riemann\u2013Liouville Fractional Integrals Using Raina\u2019s Special Function and Generalized Coordinate Convex Functions"],"prefix":"10.3390","volume":"9","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 17-01-2184, Quito, Ecuador"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0115-3079","authenticated-orcid":false,"given":"Artion","family":"Kashuri","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Technical Science, University Ismail Qemali, 1001 Vlora, Albania"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2439-8538","authenticated-orcid":false,"given":"Rozana","family":"Liko","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Technical Science, University Ismail Qemali, 1001 Vlora, Albania"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4406-5469","authenticated-orcid":false,"given":"Jorge Eliecer Hern\u00e1ndez","family":"Hern\u00e1ndez","sequence":"additional","affiliation":[{"name":"Departamento de T\u00e9cnicas Cuantitativas, Decanato de Ciencias Econ\u00f3micas y Empresariales, Universidad Centroccidental Lisandro Alvarado, Av. 20 esq. 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