Popoviciu type inequalities via Green function and Taylor polynomial. (English) Zbl 1424.26036
Summary: 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.
MSC:
| 26D07 | Inequalities involving other types of functions |
| 26D15 | Inequalities for sums, series and integrals |
| 26D20 | Other analytical inequalities |
Keywords:
Popoviciu inequality; Taylor formula; Green function; Chebyshev functional; Grüss inequality; Ostrowski inequality; exponential convexity; Cauchy meanReferences:
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