{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,6]],"date-time":"2026-05-06T05:02:02Z","timestamp":1778043722526,"version":"3.51.4"},"reference-count":24,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2022,12,8]],"date-time":"2022-12-08T00:00:00Z","timestamp":1670457600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Science, Research and Innovation Fund (NSRF), Thailand"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Recently, there has been a strong push toward creating and expanding quadrature inequalities in quantum calculus. In order to investigate various avenues for quantum inquiry, a number of quantum extensions of midpoint estimations are studied. The goal of this research article is to discover novel quantum midpoint-type inequalities that are twice q\u03be2-differentiable for (\u03b1,m)-convex functions. Firstly, we obtain novel identity for q\u03be2-integral by employing quantum calculus tools. Then by using the auxiliary identity, we formulate new bounds by taking into account the known quantum H\u00f6lder and Power mean inequalities. An example is provided with a graphical representation to show the validity of obtaining results. The outcomes of this study clarify and expand earlier research on midpoint-type inequalities. Analytic inequalities of this type as well as particularly related strategies have applications for various fields where symmetry plays an important role.<\/jats:p>","DOI":"10.3390\/sym14122599","type":"journal-article","created":{"date-parts":[[2022,12,8]],"date-time":"2022-12-08T04:05:29Z","timestamp":1670472329000},"page":"2599","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":10,"title":["New Variants of Quantum Midpoint-Type Inequalities"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7192-8269","authenticated-orcid":false,"given":"Saad Ihsan","family":"Butt","sequence":"first","affiliation":[{"name":"Department of Mathematics, Lahore Campus, COMSATS University Islamabad, Islamabad 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"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7469-5402","authenticated-orcid":false,"given":"Kamsing","family":"Nonlaopon","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen 40002, Thailand"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,12,8]]},"reference":[{"key":"ref_1","unstructured":"Ernst, T. 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