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Popoviciu type inequalities via Green function and Taylor polynomial

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 Čebyšev 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.

Popoviciu inequality; Taylor formula; Green function; Čebyšev functional; Grüss inequality; Ostrowski inequality; exponential convexity; Cauchy mean

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