{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,8]],"date-time":"2025-12-08T22:00:19Z","timestamp":1765231219197,"version":"build-2065373602"},"reference-count":42,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2021,9,1]],"date-time":"2021-09-01T00:00:00Z","timestamp":1630454400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100007345","name":"King Mongkut's University of Technology North Bangkok","doi-asserted-by":"publisher","award":["KMUTNB-63-KNOW-21"],"award-info":[{"award-number":["KMUTNB-63-KNOW-21"]}],"id":[{"id":"10.13039\/501100007345","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Quantum information theory, an interdisciplinary field that includes computer science, information theory, philosophy, cryptography, and symmetry, has various applications for quantum calculus. Inequalities has a strong association with convex and symmetric convex functions. In this study, first we establish a p,q-integral identity involving the second p,q-derivative and then we used this result to prove some new trapezoidal type inequalities for twice p,q-differentiable convex functions. It is also shown that the newly established results are the refinements of some existing results in the field of integral inequalities. 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\/sym13091605","type":"journal-article","created":{"date-parts":[[2021,9,1]],"date-time":"2021-09-01T11:39:03Z","timestamp":1630496343000},"page":"1605","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["On Some New Trapezoidal Type Inequalities for Twice (p, q) Differentiable Convex Functions in Post-Quantum Calculus"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8455-1402","authenticated-orcid":false,"given":"Thanin","family":"Sitthiwirattham","sequence":"first","affiliation":[{"name":"Mathematics Department, Faculty of Science and Technology, Suan Dusit University, Bangkok 10300, Thailand"}]},{"given":"Ghulam","family":"Murtaza","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of Management and Technology, Lahore 54700, Pakistan"}]},{"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"}]},{"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, 45110 Ioannina, Greece"},{"name":"Nonlinear Analysis and Applied Mathematics (NAAM)\u2014Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia"}]},{"given":"Muhammad","family":"Adeel","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of Management and Technology, Lahore 54700, Pakistan"}]},{"given":"Jarunee","family":"Soontharanon","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Applied Science, King Mongkut\u2019s University of Technology North Bangkok, Bangkok 10800, Thailand"}]}],"member":"1968","published-online":{"date-parts":[[2021,9,1]]},"reference":[{"key":"ref_1","unstructured":"Dragomir, S.S., and Pearce, C.E.M. 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