We firstly establish an identity for $n$ time differentiable mappings Then, a new inequality for $n$ times differentiable functions is deduced. Finally, some perturbed Ostrowski type inequalities for functions whose $n$th derivatives are of bounded variation are obtained.

We generalize Ostrowski inequality for higher order derivatives, by using a generalized Euler type identity. Some of the inequalities produced are sharp, namely attained by basic functions. The rest of the estimates are tight. We give applications to trapezoidal and mid-point rules. Estimates are given with respect to L∞ norm. c © 2006 Elsevier Ltd. All rights reserved.

A main class of inequalities including generalized Ostrowski and Ostrowski-Grüss inequalities is established in ] , [ 1 b a L and ] , [ b a L spaces. As this class can be corresponded to a weighted approximation formula, new inequalities can be obtained by using its upper and lower bounds. Some illustrative examples such as three new generalizations of Ostrowski and Ostrowski-Grüss inequalities...

Some new inequalities related to Jensen and Ostrowski inequalities for general Lebesgue integral are obtained. Applications for $f$-divergence measure are provided as well.

In this paper some new Ostrowski type inequalities for co-ordinated s-convex functions in the second sense are obtained.

On utilising an identity from [5], some weighted Ostrowski type inequalities are established.

In this paper, we provide inequalities of Jensen-Ostrowski type, by investigating the magnitude of the quantity ∫ Ω (f ◦ g) dμ− f(ζ)− ∫ Ω (g − ζ)f ′ ◦ g dμ+ 1 2 λ ∫ Ω (g − ζ) dμ, for various assumptions on the absolutely continuous function f : [a, b] → C, ζ ∈ [a, b], λ ∈ C and a μ-measurable function g on Ω. Special cases are considered to provide some inequalities of Jensen type, as well as O...

Sharp Grüss-type inequalities for functions whose derivatives are of bounded variation (Lipschitzian or monotonic) are given. Applications in relation with the well-known Čebyšev, Grüss, Ostrowski and Lupaş inequalities are provided as well.