Majorization Inequalities via Peano's Representation of Hermite's Polynomial

Abstract

The Peano's representation of Hermite polynomial and new Green functions are used to construct the identities related to the generalization of majorization type inequalities in discrete as well as continuous case. $\check{C}$eby$\check{s}$ev functional is used to find the bounds for new generalized identities and to develop the Gr$\ddot{u}$ss and Ostrowski type inequalities. Further more, we present exponential convexity together with Cauchy means for linear functionals associated with the obtained inequalities and give some applications.