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=1mρih(λi) and the integral ∫abρ(λ)h(γ(λ))dλ where h is an n-convex function. © 2019, The Author(s).