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}. 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.
Highlights
The main purpose of this note is to consider new generalizations of weighted Ostrowski type inequalities for functions presented by a Hermite interpolating polynomial
The methods used are based on the classical real analysis, application of the Hermite interpolating polynomials and the weighted Montgomery identity
We will investigate some applications of the above results in numerical analysis and probability theory
Summary
(t – a)f (t) dt + (t – b)f (t) dt , b–a a b–a a x in this paper we use the weighted Montgomery identity to obtain certain generalizations of Ostrowski type inequalities. The main purpose of this note is to consider new generalizations of weighted Ostrowski type inequalities for functions presented by a Hermite interpolating polynomial. Since a special case of the Hermite interpolating polynomial is the two-point Taylor polynomial, in this way we generalized results from paper [3], where Ostrowski type inequalities are established by using the Taylor formula. 2, we establish weighted generalizations of the Montgomery identity constructed by using the Hermite interpolating polynomial and the Green function. 3, we derive Ostrowski type inequalities for differentiable functions of class Cn. As a special case, we consider results for (m, n – m) interpolating polynomial. Inserting (17) and (18) into (16), we obtain (14)
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