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 $$\sum _{i=1}^m \rho _i h(\lambda _i)$$ ∑ i = 1 m ρ i h ( λ i ) and the integral $$\int ^{b}_{a} \rho (\lambda ) h(\gamma (\lambda ))d\lambda $$ ∫ a b ρ ( λ ) h ( γ ( λ ) ) d λ where h is an n-convex function.