{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,6]],"date-time":"2026-05-06T05:02:01Z","timestamp":1778043721062,"version":"3.51.4"},"reference-count":34,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2022,4,3]],"date-time":"2022-04-03T00:00:00Z","timestamp":1648944000000},"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-64-KNOW-36"],"award-info":[{"award-number":["KMUTNB-64-KNOW-36"]}],"id":[{"id":"10.13039\/501100007345","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>In this paper, we give the generalized version of the quantum Simpson\u2019s and quantum Newton\u2019s formula type inequalities via quantum differentiable \u03b1,m-convex functions. The main advantage of these new inequalities is that they can be converted into quantum Simpson and quantum Newton for convex functions, Simpson\u2019s type inequalities \u03b1,m-convex function, and Simpson\u2019s type inequalities without proving each separately. These inequalities can be helpful in finding the error bounds of Simpson\u2019s and Newton\u2019s formulas in numerical integration. 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\/sym14040736","type":"journal-article","created":{"date-parts":[[2022,4,3]],"date-time":"2022-04-03T06:04:01Z","timestamp":1648965841000},"page":"736","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":27,"title":["Simpson\u2019s and Newton\u2019s Type Inequalities for (\u03b1,m)-Convex Functions via Quantum Calculus"],"prefix":"10.3390","volume":"14","author":[{"given":"Jarunee","family":"Soontharanon","sequence":"first","affiliation":[{"name":"Department of Mathematics, Faculty of Applied Science, King Mongkut\u2019s University of Technology North Bangkok, Bangkok 10800, Thailand"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"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"}],"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 and Arts, Khon Kaen University, Khon Kaen 40002, Thailand"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zoya","family":"Abdullah","sequence":"additional","affiliation":[{"name":"Department of Mathematics, COMSATS University Islamabad Sahiwal Campus, Sahiwal 57000, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,4,3]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"100","DOI":"10.1007\/BF01837981","article-title":"Some remarks on s-convex functions","volume":"48","author":"Hudzik","year":"1994","journal-title":"Aequ. 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