POSITIVITY OF SUMS AND INTEGRALS FOR n−CONVEX FUNCTIONS VIA EXTENSION OF MONTGOMERY IDENTITY USING NEW GREEN FUNCTIONS

Abstract

New general linear (integral and discrete) identities and inequalities are given for convex functions of order n via extension of Montgomery identity using new Green functions. We also state positivity conditions for these inequalities. We also study n-convexity at a point for our proposed inequalities. Bounds for reminders for proposed results are also given by using Grüss- and Ostrowski-types inequalities. We would also state mean value results of Cauchy type and Lagrange type.