Ataman, CananKadakal, Mahirİşcan, İmdat2026-09-012026-09-0120221584-286Xhttps://doi.org/10.37193/CMI.2022.02.02https://hdl.handle.net/20.500.12403/8372In this paper, we introduce and study the concept of strongly n-polynomial convexity functions and their some algebraic properties. We prove two Hermite-Hadamard type inequalities for the newly introduced class of functions. In addition, we obtain some refinements of the Hermite-Hadamard inequality for functions whose first derivative in absolute value, raised to a certain power which is greater than one, respectively at least one, is strongly n-polynomial convexity. Also, we compare the obtained results with both Hölder, Hölder-İşcan inequalities and power-mean, improved-power-mean integral inequalities and show that the result obtained with Hölder-İşcan and improved power-mean inequalities give better approach than the others. © 2022, SINUS Association. All rights reserved.eninfo:eu-repo/semantics/openAccessConvex FunctionHermite-Hadamard InequalityHölder Integral InequalityHölder İşcan Integral InequalityStrongly N-Polynomial ConvexityArticle31215517210.37193/CMI.2022.02.022-s2.0-85185964382Q4