ON GENERALIZATIONS OF MAJORIZATION INEQUALITY

Abstract

In this paper, we give some identities for the difference of majorization inequality by using Abel-Gontscharoff’s interpolating polynomials and conditions on Green’s functions as well as present the generalizations of majorization theorem for the class of n-convex func- tions. We obtain the generalizations of classical and weighted majorization theorems. We give bounds for identities related to the generalizations of majorization inequalities by using Čebyšev functionals. We also give Grüss type inequalities and Ostrowski-type inequalities for these functionals. We present mean value theorems and n-exponential convexity which leads to exponential convexity and then log-convexity for these functionals. At the end, we discuss some families of functions which enable us to construct a large families of functions that are exponentially convex and also give Stolarsky type means with their monotonicity.