{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,5]],"date-time":"2026-01-05T04:53:25Z","timestamp":1767588805531,"version":"build-2065373602"},"reference-count":38,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2022,4,1]],"date-time":"2022-04-01T00:00:00Z","timestamp":1648771200000},"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>Quantum calculus has numerous applications in mathematics. This novel class of functions may be used to produce a variety of conclusions in convex analysis, special functions, quantum mechanics, related optimization theory, and mathematical inequalities. It can drive additional research in a variety of pure and applied fields. This article\u2019s main objective is to introduce and study a new class of preinvex functions, which is called higher-order generalized strongly n-polynomial preinvex function. We derive a new q1q2-integral identity for mixed partial q1q2-differentiable functions. Because of the nature of generalized convexity theory, there is a strong link between preinvexity and symmetry. Utilizing this as an auxiliary result, we derive some estimates of upper bound for functions whose mixed partial q1q2-differentiable functions are higher-order generalized strongly n-polynomial preinvex functions on co-ordinates. Our results are the generalizations of the results in earlier papers. Quantum inequalities of this type and the techniques used to solve them have applications in a wide range of fields where symmetry is important.<\/jats:p>","DOI":"10.3390\/sym14040717","type":"journal-article","created":{"date-parts":[[2022,4,1]],"date-time":"2022-04-01T21:23:55Z","timestamp":1648848235000},"page":"717","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["q1q2-Ostrowski-Type Integral Inequalities Involving Property of Generalized Higher-Order Strongly n-Polynomial Preinvexity"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5835-3349","authenticated-orcid":false,"given":"Humaira","family":"Kalsoom","sequence":"first","affiliation":[{"name":"Department of Mathematics, Zhejiang Normal University, Jinhua 321004, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1567-0264","authenticated-orcid":false,"given":"Miguel","family":"Vivas-Cortez","sequence":"additional","affiliation":[{"name":"Escuela de Ciencias F\u00edsicas y Matem\u00e1ticas, Facultad de Ciencias Naturales y Exactas, Pontificia Universidad Cat\u00f3lica del Ecuador, Sede Quito 17-01-2184, Ecuador"}]}],"member":"1968","published-online":{"date-parts":[[2022,4,1]]},"reference":[{"key":"ref_1","first-page":"193","article-title":"On a q-definite integrals","volume":"4","author":"Jackson","year":"1910","journal-title":"Quart. 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