{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,2]],"date-time":"2026-04-02T01:30:09Z","timestamp":1775093409942,"version":"3.50.1"},"reference-count":33,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2022,7,6]],"date-time":"2022-07-06T00:00:00Z","timestamp":1657065600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["62002079"],"award-info":[{"award-number":["62002079"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>This study provokes the existence of quantum Hermite-Hadamard inequalities under the concept of q-integral. We analyse and illustrate a new identity for the differentiable function mappings whose second derivatives in absolute value are (\u03b1,m) convex. Some basic inequalities such as H\u00f6lder\u2019s and Power mean have been used to obtain new bounds and it has been determined that the main findings are generalizations of many results that exist in the literature. We make links between our findings and a number of well-known discoveries in the literature. The conclusion in this study unify and generalise previous findings on Hermite-Hadamard inequalities.<\/jats:p>","DOI":"10.3390\/sym14071394","type":"journal-article","created":{"date-parts":[[2022,7,6]],"date-time":"2022-07-06T21:15:52Z","timestamp":1657142152000},"page":"1394","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":12,"title":["New Estimates for Hermite-Hadamard Inequality in Quantum Calculus via (\u03b1, m) Convexity"],"prefix":"10.3390","volume":"14","author":[{"given":"Peng","family":"Xu","sequence":"first","affiliation":[{"name":"School of Computer Science of Information Technology, Qiannan Normal University for Nationalities, Duyun 558000, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7192-8269","authenticated-orcid":false,"given":"Saad","family":"Ihsan Butt","sequence":"additional","affiliation":[{"name":"Department of Mathematics, COMSATS University Islamabad, Lahore Campus, Lahore 54000, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Qurat Ul","family":"Ain","sequence":"additional","affiliation":[{"name":"Department of Mathematics, COMSATS University Islamabad, Lahore Campus, Lahore 54000, Pakistan"}],"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"}]}],"member":"1968","published-online":{"date-parts":[[2022,7,6]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Ernst, T. 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