Strongly n-polynomial convexity and related inequalities

In 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.