{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T02:10:12Z","timestamp":1760235012692,"version":"build-2065373602"},"reference-count":42,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2021,7,7]],"date-time":"2021-07-07T00:00:00Z","timestamp":1625616000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100004396","name":"Thailand Research Fund","doi-asserted-by":"publisher","award":["RSA6180059"],"award-info":[{"award-number":["RSA6180059"]}],"id":[{"id":"10.13039\/501100004396","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>In this paper, the notions of post-quantum integrals for two-variable interval-valued functions are presented. The newly described integrals are then used to prove some new Hermite\u2013Hadamard inclusions for co-ordinated convex interval-valued functions. Many of the findings in this paper are important extensions of previous findings in the literature. Finally, we present a few examples of our new findings. Analytic inequalities of this nature and especially the techniques involved have applications in various areas in which symmetry plays a prominent role.<\/jats:p>","DOI":"10.3390\/sym13071216","type":"journal-article","created":{"date-parts":[[2021,7,8]],"date-time":"2021-07-08T04:32:49Z","timestamp":1625718769000},"page":"1216","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["Hermite\u2013Hadamard Inclusions for Co-Ordinated Interval-Valued Functions via Post-Quantum Calculus"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-8185-3539","authenticated-orcid":false,"given":"Jessada","family":"Tariboon","sequence":"first","affiliation":[{"name":"Intelligent and Nonlinear Dynamic Innovations Research Center, Department of Mathematics, Faculty of Applied Science, King Mongkut\u2019s University of Technology North Bangkok, Bangkok 10800, Thailand"}],"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 for NSLSCS, School of Mathematical Sciences, Nanjing Normal University, Nanjing 210023, China"}],"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\/0000-0002-7695-2118","authenticated-orcid":false,"given":"Sotiris K.","family":"Ntouyas","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of Ioannina, 451 10 Ioannina, Greece"},{"name":"Nonlinear Analysis and Applied Mathematics (NAAM)-Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,7,7]]},"reference":[{"key":"ref_1","first-page":"193","article-title":"On q-definite integrals","volume":"41","author":"Jackson","year":"1910","journal-title":"Quart. J. Pure Appl. Math."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1155\/2011\/107384","article-title":"Boundary-value problems for nonlinear third-order q-difference equations","volume":"2011","author":"Ahmad","year":"2011","journal-title":"Electron. J. Differ. Equ."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"35","DOI":"10.1186\/1687-1847-2012-35","article-title":"A study of second-order q-difference equations with boundary conditions","volume":"2012","author":"Ahmad","year":"2012","journal-title":"Adv. Differ. 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