Positivity of sums and integrals for n-convex functions via the Fink identity.

We consider the positivity of the sum Σi=1n ρiF(ξi), where F is a convex function of higher order, as well as analogous results involving the integral ∫aobo ρ(ξ)F(g(ξ))dξ . We use a representation of the function F via the Fink identity and the Green function that leads us to identities from which we obtain conditions for positivity of the above-mentioned sum and integral. We also obtain bounds for the integral remainders which occur in these identities, as well as corresponding mean value results. [ABSTRACT FROM AUTHOR]