Muhammad TariqHijaz AhmadHŸseyin BudakSoubhagya Kumar SahooThanin SitthiwiratthamJiraporn Reunsumrit2025-03-102025-03-102021Axioms2075168010.3390/axioms100403282-s2.0-85121627292https://repository.dusit.ac.th//handle/123456789/4699The principal objective of this article is to introduce the idea of a new class of n-polynomial convex functions which we call n-polynomial s-type m-preinvex function. We establish a new variant of the well-known HermiteÐHadamard inequality in the mode of the newly introduced concept. To add more insight into the newly introduced concept, we have discussed some algebraic properties and examples as well. Besides, we discuss a few new exceptional cases for the derived results, which make us realize that the results of this paper are the speculations and expansions of some recently known outcomes. The immeasurable concepts and chasmic tools of this paper may invigorate and revitalize additional research in this mesmerizing and absorbing field. © 2021 by the authors. Licensee MDPI, Basel, Switzerland.All Open Access; Gold Open AccessHšlderÐêscan inequalityHšlderÕs inequalityImproved power-mean integral inequalityM-preinvex functionPower-mean integral inequalityPreinvex functionS-type convex functionArticleScopus