{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,15]],"date-time":"2026-05-15T20:42:43Z","timestamp":1778877763302,"version":"3.51.4"},"reference-count":45,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2024,8,6]],"date-time":"2024-08-06T00:00:00Z","timestamp":1722902400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"King Saud University, Riyadh, Saudi Arabia","award":["RSP2024R158"],"award-info":[{"award-number":["RSP2024R158"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>In this paper, we derive a new generic equality for the first-order differentiable functions. Through the utilization of the general identity and convex functions, we produce a family of upper bounds for numerous integral inequalities like Ostrowski\u2019s inequality, trapezoidal inequality, midpoint inequality, Simpson\u2019s inequality, Newton-type inequalities, and several two-point open trapezoidal inequalities. Also, we provide the numerical and visual explanation of our principal findings. Later, we provide some novel applications to the theory of means, special functions, error bounds of composite quadrature schemes, and parametric iterative schemes to find the roots of linear functions. Also, we attain several already known and new bounds for different values of \u03b3 and parameter \u03be.<\/jats:p>","DOI":"10.3390\/axioms13080533","type":"journal-article","created":{"date-parts":[[2024,8,6]],"date-time":"2024-08-06T15:24:16Z","timestamp":1722957856000},"page":"533","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Some Classical Inequalities Associated with Generic Identity and Applications"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5212-6252","authenticated-orcid":false,"given":"Muhammad Zakria","family":"Javed","sequence":"first","affiliation":[{"name":"Department of Mathematics, Government College University, Faisalabad 38000, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Muhammad Uzair","family":"Awan","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Government College University, Faisalabad 38000, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2160-4159","authenticated-orcid":false,"given":"Bandar","family":"Bin-Mohsin","sequence":"additional","affiliation":[{"name":"Department of Mathematics, College of Science, King Saud University, Riyadh 11451, Saudi Arabia"}],"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\/0000-0003-2902-6805","authenticated-orcid":false,"given":"Silvestru Sever","family":"Dragomir","sequence":"additional","affiliation":[{"name":"Mathematics, College of Engineering & Science, Victoria University, P.O. Box 14428, Melbourne City, VIC 8001, Australia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2024,8,6]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"91","DOI":"10.1016\/S0893-9659(98)00086-X","article-title":"Two inequalities for differentiable mappings and applications to special means of real numbers and to trapezoidal formula","volume":"11","author":"Dragomir","year":"1998","journal-title":"Appl. Math. Lett."},{"key":"ref_2","first-page":"1473","article-title":"On some inequalities for h-convex functions","volume":"4","author":"Latif","year":"2010","journal-title":"Int. J. Math. Anal."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"184","DOI":"10.1186\/1029-242X-2013-184","article-title":"Hermite-Hadamard-type inequalities for (g, \u03d5, h)-convex dominated functions","volume":"2013","author":"Ozdemir","year":"2013","journal-title":"J. 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