On some dynamic inequalities of Ostrowski, trapezoid, and Grüss type on time scales

Weighted Ostrowski, Trapezoid and Grüss Type Inequalities on Time Scales

In this paper we first derive a weighted Montgomery identity on time scales and then establish weighted Ostrowski, trapezoid and Grüss type inequalities on time scales, respectively. These results not only provide a generalization of the known results, but also give some other interesting inequalities on time scales as special cases.

Some generalized Ostrowski-Grüss type integral inequalities

An Ostrowski-Grüss type inequality on time scales

for all x ∈ [a, b]. This inequality is a connection between the Ostrowski inequality [12] and the Grüss inequality [13]. It can be applied to bound some special mean and some numerical quadrature rules. For other related results on the similar integral inequalities please see the papers [6, 10, 11, 14] and the references therein. The aim of this paper is to extend a generalizations of Ostrowski...

Ostrowski Inequalities on Time Scales

We prove Ostrowski inequalities (regular and weighted cases) on time scales and thus unify and extend corresponding continuous and discrete versions from the literature. We also apply our results to the quantum calculus case.

Grüss type inequalities for double integrals on time scales

We prove some weighted Grüss type inequalities for double integrals on time scales and unify the corresponding continuous and discrete versions, which are the generalizations of the results proved earlier in the literature