Kadakal, MahirIscan, ImdatKadakal, Huriye2026-02-282026-02-2820242651-477Xhttps://doi.org/10.15672/hujms.1310861https://search.trdizin.gov.tr/tr/yayin/detay/1289723https://hdl.handle.net/20.500.12403/6127In this paper, we first construct a new generalization of n-polynomial convex function. That is, this study is a generalization of the definition of n-polynomial convexity previously found in the literature. By making use of this construction, we derive certain inequalities for this new generalization and show that the first derivative in absolute value corresponds to a new class of n-polynomial convexity. Also, we see that the obtained results in the paper while comparing with H & ouml;lder, H & ouml;lder-& Idot;& scedil;can and power-mean, improvedpower-mean integral inequalities show that the results give a better approach than the others. Finally, we conclude our paper with applications containing some means.eninfo:eu-repo/semantics/openAccessconvex functionn-polynomial convexitygeneralized n-polynomial convexityHermite-Hadamard inequalityH & ouml;lder-& Idot;& scedil;can integral inequalityArticle5361529154110.15672/hujms.13108612-s2.0-85215311974Q21289723WOS:001385922500003Q2