{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,21]],"date-time":"2026-02-21T11:25:49Z","timestamp":1771673149285,"version":"3.50.1"},"reference-count":45,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2022,3,8]],"date-time":"2022-03-08T00:00:00Z","timestamp":1646697600000},"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>In this paper, we give some correct quantum type Simpson\u2019s inequalities via the application of q-H\u00f6lder\u2019s inequality. The inequalities of this study are compatible with famous Simpson\u2019s 1\/8 and 3\/8 quadrature rules for four and six panels, respectively. Several special cases from our results are discussed in detail. A counter example is presented to explain the limitation of H\u00f6lder\u2019s inequality in the quantum framework.<\/jats:p>","DOI":"10.3390\/sym14030548","type":"journal-article","created":{"date-parts":[[2022,3,9]],"date-time":"2022-03-09T01:50:53Z","timestamp":1646790653000},"page":"548","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["New Simpson\u2019s Type Estimates for Two Newly Defined Quantum Integrals"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7966-0471","authenticated-orcid":false,"given":"Muhammad","family":"Raees","sequence":"first","affiliation":[{"name":"School of Natural Sciences, National University of Sciences and Technology, H-12, Islamabad 44000, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Matloob","family":"Anwar","sequence":"additional","affiliation":[{"name":"School of Natural Sciences, National University of Sciences and Technology, H-12, Islamabad 44000, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"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 Exactas y Naturales, Pontificia Universidad Cat\u00f3lica del Ecuador, Av. 12 de Octubre 1076, Apartado, Quito 17-01-2184, Ecuador"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"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 Vlora, Albania"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8480-2817","authenticated-orcid":false,"given":"Muhammad","family":"Samraiz","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of Sargodha, Sargodha 40100, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2728-7537","authenticated-orcid":false,"given":"Gauhar","family":"Rahman","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics, Hazara University, Mansehra 21300, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,3,8]]},"reference":[{"key":"ref_1","first-page":"533","article-title":"On Simpson\u2019s inequality and applications","volume":"5","author":"Dragomir","year":"2000","journal-title":"J. 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