GENERALIZATION OF MAJORIZATION THEOREM BY HERMITE’S POLYNOMIAL

In this paper, we give the generalizations of majorization inequalities by using Hermite interpolating polynomial. We discuss the results for particular cases namely, Lagrange interpolating polynomial, (m, n−m) interpolating polynomial, two-point Taylor interpolating polynomial. We give bounds for the identities related to the generalizations of majorization inequalities by using ˇCebyˇsev functionals. We also give Gr¨uss 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. We give some families of functions which enable us to construct a large families of functions that are exponentially convex and also give Stolarsky type means.