Extrapolation of (p, h)-convex functions

Abstract

In recent years, some interesting multi-term refinements of interpolated and extrapolated Jensen-type inequalities for convex functions have been established. The main objective of this paper is to utilize new techniques for generalizing these types of inequalities to (p, h)-convex functions. Some improvements of inequalities arising from the new characterization of this class of functions are also discussed. The significance of these results lies in the way they extend known results from the setting of convex functions to other classes of functions.