{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T19:14:23Z","timestamp":1740165263605,"version":"3.37.3"},"reference-count":33,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2021,10,29]],"date-time":"2021-10-29T00:00:00Z","timestamp":1635465600000},"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":"The main motivation of this article is derive a new post-quantum integral identity using twice (p, q)-differentiable functions. Using the identity as an auxiliary result, we will obtain some new variants of Hermite\u2013Hadamard\u2019s inequality essentially via the class of \u03c8-preinvex functions. To support our results, we offer some applications to a special means of positive real numbers and twice (p, q)-differentiable functions that are in absolute value bounded as well.<\/jats:p>","DOI":"10.3390\/axioms10040283","type":"journal-article","created":{"date-parts":[[2021,11,1]],"date-time":"2021-11-01T15:47:38Z","timestamp":1635781658000},"page":"283","source":"Crossref","is-referenced-by-count":4,"title":["Some New Post-Quantum Integral Inequalities Involving Twice (p, q)-Differentiable \u03c8-Preinvex Functions and Applications"],"prefix":"10.3390","volume":"10","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, Quito 17-01-2184, Ecuador"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1019-9485","authenticated-orcid":false,"given":"Muhammad Uzair","family":"Awan","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Government College University, Faisalabad 38000, Pakistan"}]},{"given":"Sadia","family":"Talib","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Government College University, Faisalabad 38000, Pakistan"}]},{"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 \u201cIsmail Qemali\u201d, 9400 Vlor\u00eb, Albania"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6105-2435","authenticated-orcid":false,"given":"Muhammad Aslam","family":"Noor","sequence":"additional","affiliation":[{"name":"Department of Mathematics, COMSATS University Islamabad, Islamabad 44000, Pakistan"}]}],"member":"1968","published-online":{"date-parts":[[2021,10,29]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"489","DOI":"10.1007\/s00605-017-1039-9","article-title":"Oscillation criteria for second-order superlinear Emden-Fowler neutral differential equations","volume":"3","author":"Li","year":"2017","journal-title":"Monatsh. 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