{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,13]],"date-time":"2026-07-13T16:17:43Z","timestamp":1783959463153,"version":"3.55.0"},"reference-count":40,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2019,12,12]],"date-time":"2019-12-12T00:00:00Z","timestamp":1576108800000},"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, the study is focused on the quantum estimates of Ostrowski type inequalities for q-differentiable functions involving the special function introduced by R.K. Raina which depends on certain parameters. Our methodology involves Jackson\u2019s q-integral, the basic concepts of quantum calculus, and a generalization of a class of special functions used in the frame of convex sets and convex functions. As a main result, some quantum estimates for the aforementioned inequality are established and some cases involving the special hypergeometric and Mittag\u2013Leffler functions have been studied and some known results are deduced.<\/jats:p>","DOI":"10.3390\/sym11121513","type":"journal-article","created":{"date-parts":[[2019,12,12]],"date-time":"2019-12-12T11:06:41Z","timestamp":1576148801000},"page":"1513","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":20,"title":["Quantum Estimates of Ostrowski Inequalities for Generalized \u03d5-Convex Functions"],"prefix":"10.3390","volume":"11","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1567-0264","authenticated-orcid":false,"given":"Miguel J.","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":[{"vocabulary":"crossref","role":"author"}]},{"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, L. Pavaresia, Vlora 1001, Albania"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"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, L. Pavaresia, Vlora 1001, Albania"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4406-5469","authenticated-orcid":false,"given":"Jorge E. 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. Av. Moran, Edf. Los Militares, Piso 2, Ofc.2, Barquisimeto 3001, Venezuela"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2019,12,12]]},"reference":[{"key":"ref_1","first-page":"193","article-title":"On a q-definite integrals","volume":"41","author":"Jackson","year":"1910","journal-title":"Q. J. Pure Appl. Math."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"81","DOI":"10.3176\/proc.2008.2.03","article-title":"The different tongues of q-calculus","volume":"57","author":"Ernst","year":"2008","journal-title":"Proc. Eston. Acad. Sci."},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Ernst, T. (2012). 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