On <i>n</i>-Polynomial convexity and some related inequalities
Tekin Toplu, Mahir Kadakal, İmdat Işcan
Abstract
In this paper, we introduce and study the concept of <i>n</i>-polynomial convexity functions and their some algebric 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 <i>n</i>-polynomial convexity. Also, we compare the results obtained 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. Some applications to special means of real numbers are also given.