Weighted averages of n-convex functions via extension of Montgomery's identity.

Using an extension of Montgomery's identity and the Green's function, we obtain new identities and related inequalities for weighted averages of n-convex functions, i.e. the sum ∑ i = 1 m ρ i h (λ i) and the integral ∫ a b ρ (λ) h (γ (λ)) d λ where h is an n-convex function. [ABSTRACT FROM AUTHOR]