Popoviciu type inequalities via Green function and Taylor polynomial

Abstract

The well-known Taylor polynomial is used to construct the identities coming from Popoviciu type inequalities for convex functions via the Green function. The bounds for the new identities are found using the Çebyşev functional to develop the Grüss and Ostrowski type inequalities. Further, more exponential convexity together with Cauchy means is presented for linear functionals associated with the obtained inequalities.