{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:52:52Z","timestamp":1760147572292,"version":"build-2065373602"},"reference-count":24,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2023,2,13]],"date-time":"2023-02-13T00:00:00Z","timestamp":1676246400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Deanship of Scientific Research (DR) at King Abdulaziz University (KAU)","award":["RG-7-130-43"],"award-info":[{"award-number":["RG-7-130-43"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>It is the purpose of this paper to propose a novel class of convex functions associated with strong \u03b7-convexity. A relationship between the newly defined function and an earlier generalized class of convex functions is hereby established. To point out the importance of the new class of functions, some examples are presented. Additionally, the famous Hermite\u2013Hadamard inequality is derived for this generalized family of convex functions. Furthermore, some inequalities and results for strong \u03b7-convex function are also derived. We anticipate that this new class of convex functions will open the research door to more investigations in this direction.<\/jats:p>","DOI":"10.3390\/axioms12020195","type":"journal-article","created":{"date-parts":[[2023,2,13]],"date-time":"2023-02-13T02:14:11Z","timestamp":1676254451000},"page":"195","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["A New Advanced Class of Convex Functions with Related Results"],"prefix":"10.3390","volume":"12","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5373-4663","authenticated-orcid":false,"given":"Muhammad Adil","family":"Khan","sequence":"first","affiliation":[{"name":"Department of Mathematics, University of Peshawar, Peshawar 25000, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"family":"Adnan","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of Peshawar, Peshawar 25000, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0170-5286","authenticated-orcid":false,"given":"Tareq","family":"Saeed","sequence":"additional","affiliation":[{"name":"Financial Mathematics and Actuarial Science (FMAS)-Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1375-1474","authenticated-orcid":false,"given":"Eze R.","family":"Nwaeze","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Computer Science, Alabama State University, Montgomery, AL 36101, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,2,13]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Niculescu, C.P., and Persson, L.E. (2018). Convex Functions and Their Applications. A Contemporary Approach, Springer. [2nd ed.]. 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