Marko Matić

Improvement and further generalization of inequalities of Ostrowski-Grüss type

Abstract We improve some inequalities of Ostrowski-Gruss type and further generalize them. We apply the obtained results to the estimation of error bounds for some numerical quadrature rules. Also, some bounds for the differences of some special means are discussed.

Improvement of some inequalities of Euler-Grüss type

Abstract We prove an inequality of Gruss type and use it to improve strictly some general Euler-Gruss type inequalities: All improved inequalities are sharp.

Generalizations of weighted version of Ostrowski's inequality and some related results.

We establish some new weighted integral identities and use them to prove a number of inequalities of Ostrowski type. Among other results, we generalize one result related to the weighted version of the Ostrowskis inequality of Pecaric and Savic (Zbornik radova VAKoV (Beograd), 9(1983), 171-202) as well as the recent result of Roumeliotis et al. (RGMIA, 1(1)(1998)). We also show that the recent Anastassious generalization (Proc. Amer. Math. Soc., 123(1995), 3775-3781) of the Ostrowskis inequality is a special case of some results from this paper.

ON EULER MIDPOINT FORMULAE

Modified versions of the Euler midpoint formula are given for functions whose derivatives are either functions of bounded variation, Lipschitzian functions or functions in L p -spaces. The results are applied to quadrature formulae.

Some inequalities of euler-grüss type

Abstract Applying the Gruss inequality to the Euler type formulae we prove some Euler-Gruss-type inequalities.

On generalizations of Ostrowski inequality via Euler harmonic identities.

Some generalizations of Ostrowski inequality are given, by using some Euler identities involving harmonic sequences of polynomials.

Two-point formulae of Euler type

An analysis is made of quadrature via two-point formulae when the integrand is Lipschitz or of bounded variation. The error estimates are shown to be as good as those found in recent studies using Simpson (three-point) formulae.

Refinements of some bounds in information theory

Recently Dragomir and Goh have produced some interesting new bounds relating to entropy measures in information theory. We establish several refinements of their results.

INEQUALITIES OF HLAWKA'S TYPE IN n-INNER PRODUCT SPACES

In this paper, we give Hlawkas type inequalities and related results in n-inner product spaces.

Generalizations of the Jensen-Steffensen and related inequalities

We present a couple of general inequalities related to the Jensen-Steffensen inequality in its discrete and integral form. The Jensen-Steffensen inequality, Slater’s inequality and a generalization of the counterpart to the Jensen-Steffensen inequality are deduced as special cases from these general inequalities.