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Generalizations of Sherman's inequality by Hermite's interpolating polynomial

Generalizations of Sherman's inequality for convex functions of higher order are obtained by applying Hermite's interpolating polynomials. The results for particular cases, namely, Lagrange, (m, n-m) and two-point Taylor interpolating polynomials are also cosidered. The Grüss and Ostrowski type inequalities related to these generalizations are given.

majorization; n-convexity; Schur-convexity; Sherman's theorem; Hermite's interpolating polynomial; Chebyshev functional; Grüss type inequalities; Ostrowski type inequalities; exponentially convex functions; log-convex functions; means

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