Ihsan Butt, SaadBudak, HuseyinTariq, MuhammadNadeem, Muhammad2021-12-012021-12-0120210170-42141099-1476https://doi.org/10.1002/mma.7465https://hdl.handle.net/20.500.12684/10428In this present paper, we introduce the idea and concept of n-polynomial s-type preinvex functions. We elaborate and investigate the algebraic properties of the newly introduced definition and discuss their connections and relations with convex functions. We find the new sort of Hermite-Hadamard inequality via a newly introduced definition. Furthermore, some refinements of Hermite-Hadamard inequality are given. Finally, we investigated some applications via this newly introduced definition. The results obtained in this paper can be viewed as significant improvement of previously known results.en10.1002/mma.7465info:eu-repo/semantics/closedAccessH&#246lder&aposs inequalityH&#246lder&#8211&#205scan inequalityimproved power mean integral inequalityn&#8208polynomial s&#8208type preinvexitypreinvex functions&#8208type preinvexityGenerationConvexityInvexityArticle441411006110212-s2.0-85105631491WOS:000649589100001Q1Q1