Weighted majorization inequalities for <italic>n</italic>-convex functions via extension of Montgomery identity using Green function.

New identities and inequalities are given for weighted majorization theorem for <italic>n</italic>-convex functions by using extension of the Montgomery identity and Green function. Various bounds for the reminders in new generalizations of weighted majorization formulae are provided using Čebyšev type inequalities. Mean value theorems are also discussed for functional related to new results. [ABSTRACT FROM AUTHOR]