Construction of a new class of functions with their some properties and certain inequalities: n-fractional polynomial convex functions

Abstract

. In this paper, we introduce a new function class called n -fractional polynomial convex function and their some algebric properties. We obtain some refinements of the right-hand side of Hermite-Hadamard inequality for the class of functions whose derivatives in absolutely value at certain powers are n -fractional polynomial convex. Also, we compare the results obtained with both H¨older, H¨older-˙Is¸can inequalities and power-mean, improved-power-mean integral inequalities and show that the result obtained with H¨older-˙Is¸can and improved power-mean inequalities give better approach than the others. Some applications to special means of real numbers are also given.