Generalizations of Ostrowski type inequalities via Hermite polynomials

Abstract

We present new generalizations of the weighted Montgomery identity constructed by using the Hermite interpolating polynomial. The obtained identities are used to establish new generalizations of weighted Ostrowski type inequalities for differentiable functions of class $C^{n}$ C n . Also, we consider new bounds for the remainder of the obtained identities by using the Chebyshev functional and certain Grüss type inequalities for this functional. By applying those results we derive inequalities for the class of n-convex functions.

On Ostrowski Type Inequalities via the Extended Version of Montgomery’s Identity

“…Some other Ostrowski type inequalities can be spotted in [5,[12][13][14]. Some recently obtained generalizations of Ostrowski type inequalities via weighted generalizations of the Montgomery identity established by using the Hermite interpolating polynomial and Green's functions can be found in [15].…”