HERMITE INTERPOLATION WITH GREEN FUNCTIONS AND POSITIVITY OF GENERAL LINEAR INEQUALITIES FOR n-CONVEX FUNCTIONS

We state new general linear identities and inequalities involving n-convex functions using Hermite interpolation polynomials and Green functions. We also study positivity conditions of our stated inequalities. Moreover, we state related inequalities for n-convex functions at a point. Bounds for the reminders in new generalizations of general linear inequalities are given by using Cebysev functional, Ostrowski- and Gruss- types inequalities.