{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T02:43:02Z","timestamp":1760150582296,"version":"build-2065373602"},"reference-count":35,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2023,12,8]],"date-time":"2023-12-08T00:00:00Z","timestamp":1701993600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Scientific Research Deanship at University of Ha\u2019il\u2014Saudi Arabia","award":["RG-23 036"],"award-info":[{"award-number":["RG-23 036"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>In this article, closed Newton\u2013Cotes-type symmetrical inequalities involving four-point functions whose second derivatives are (s,m)-preinvex in the second sense are established. Some applications to quadrature formulas as well as inequalities involving special means are provided.<\/jats:p>","DOI":"10.3390\/sym15122178","type":"journal-article","created":{"date-parts":[[2023,12,11]],"date-time":"2023-12-11T06:56:00Z","timestamp":1702277760000},"page":"2178","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Some Simpson-like Inequalities Involving the (s,m)-Preinvexity"],"prefix":"10.3390","volume":"15","author":[{"given":"Tarek","family":"Chiheb","sequence":"first","affiliation":[{"name":"Laboratory of Analysis and Control of Differential Equations \u201cACED\u201d, Department of Mathematics, Facuty MISM, University of 8 May 1945 Guelma, P.O. Box 401, Guelma 24000, Algeria"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Badreddine","family":"Meftah","sequence":"additional","affiliation":[{"name":"Laboratory of Analysis and Control of Differential Equations \u201cACED\u201d, Department of Mathematics, Facuty MISM, University of 8 May 1945 Guelma, P.O. Box 401, Guelma 24000, Algeria"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Abdelkader","family":"Moumen","sequence":"additional","affiliation":[{"name":"Department of Mathematics, College of Science, University of Ha\u2019il, P.O. Box 2240, Ha\u2019il 55473, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mouataz Billah","family":"Mesmouli","sequence":"additional","affiliation":[{"name":"Department of Mathematics, College of Science, University of Ha\u2019il, P.O. Box 2240, Ha\u2019il 55473, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mohamed","family":"Bouye","sequence":"additional","affiliation":[{"name":"Department of Mathematics, College of Science, King Khalid University, P.O. Box 9004, Abha 61413, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,12,8]]},"reference":[{"key":"ref_1","first-page":"54","article-title":"Hermite-Hadamard\u2019s inequalities for functions whose first derivatives are (s,m)-preinvex in the second sense","volume":"10","author":"Meftah","year":"2016","journal-title":"J. New Theory"},{"key":"ref_2","unstructured":"Pe\u0107arixcx, J.E., Proschan, F., and Tong, Y.L. (1992). Mathematics in Science and Engineering, Academic Press, Inc."},{"key":"ref_3","unstructured":"Toader, G. (1984, January 25\u201327). Some generalizations of the convexity. 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