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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.

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