Ozcan, SerapKadakal, MahirIscan, ImdatKadakal, Huriye2026-02-282026-02-2820241844-95812068-3049https://doi.org/10.46939/J.Sci.Arts-24.4-a07https://hdl.handle.net/20.500.12403/6208In this paper, we introduce the notion of generalized n-polynomial Pfunction. We explore some algebraic properties of this function class. Additionally, we establish a new trapezium type inequality for this generalized class of functions and derive several refinements of the trapezium type inequality for functions whose first derivative in absolute value at a certain power is generalized n-polynomial P-function. Finally, we conclude our paper by exploring some applications of the results we have obtained in the context of special means. Our novel findings generalize previously known results in the literature.eninfo:eu-repo/semantics/openAccessConvex functionn-polynomial harmonically convexitygeneralized n-polynomial harmonically convexityHermite-Hadamard inequalityintegral inequalitiesArticle484385410.46939/J.Sci.Arts-24.4-a07WOS:001386506200007Q4