In this paper, we establish a weighted Ostrowski Grüss type inequality for twice differentiable mappings in terms of lower and upper bounds of the second derivative. Applications in numerical integration are also given.

A companion for the Ostrowski and the generalised trapezoid inequalites for various classes of functions, including functions of bounded variation, Lipschitzian, convex and absolutely continuous functions is established. Applications for weighted means are also given.

Discrete versions of Ostrowski’s inequality for vectors in normed linear spaces are given.

We disprove and correct some recently obtained results regarding Montgomery identity for quantum integral operator Ostrowski type inequalities involving convex functions.

In this paper we consider a numeration system, originally due to Ostrowski, based on the continued fraction expansion of a real number α. We prove that this system has deep connections with the Sturmian graph associated with α. We provide several properties of the representations of the natural integers in this system. In particular, we prove that the set of lazy representations of the natural ...

We give upper and lower bounds on the determinant of a perturbation of the identity matrix or, more generally, a perturbation of a nonsingular diagonal matrix. The matrices considered are, in general, diagonally dominant. The lower bounds are best possible, and in several cases they are stronger than well-known bounds due to Ostrowski and other authors. If A = I−E is a real n×n matrix and the e...

Here first we collect and develop necessary background on time scales required for this article. Then we present time scales integral inequalities of types: Poincaré, Sobolev, Opial, Ostrowski and Hilbert–Pachpatte. We give also the generalized analogs of all these inequalities involving high order delta derivatives of functions on time scales. We finish with lots of applications: all these ine...