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

Abstract

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=1mρih(λi) and the integral $$\\int ^{b}_{a} \\rho (\\lambda ) h(\\gamma (\\lambda ))d\\lambda $$∫abρ(λ)h(γ(λ))dλ where h is an n-convex function.