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

İmdat İşcan;


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 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.

Vol. 24 (2023), No. 3, pp. 1389-1404
DOI: 10.18514/MMN.2023.4142

Download: MMN-4142