Some Ostrowski and trapezoid type inequalities for the Stieltjes integral in the case of Lipschitzian integrators for both Hölder continuous and monotonic integrals are obtained. The dual case is also analysed. Applications for the midpoint rule are pointed out as well.
On the Ostrowski’s inequality for Riemann-Stieltjes integral and applications
✍ Scribed by Dragomir, S. S.
- Publisher
- Springer-Verlag
- Year
- 2000
- Tongue
- English
- Weight
- 171 KB
- Volume
- 7
- Category
- Article
- ISSN
- 1226-0061
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📜 SIMILAR VOLUMES
Some Ostrowski type inequalities are given for the Stieltjes integral where the integrand is absolutely continuous while the integrator is of bounded variation. The case when | f | is convex is explored. Applications for the mid-point rule and a generalised trapezoid type rule are also presented.
Utilising the Beesack version of the Darst-Pollard inequality, some error bounds for approximating the Riemann-Stieltjes integral are given. Some applications related to the trapezoid and mid-point quadrature rules are provided.
A new generalization of Ostrowski's integral inequality is established. A consequence of the generalization is that we can derive new estimates for the remainder term of the midpoint, trapezoid, and Simpson formulae. These estimates are improvements of some recently obtained estimates. Applications
## Some new bounds for the first inequality of Ostrowsld-Griiss type are derived. These new bounds can be much better than some recently obtained bounds. Applications in numerical integration are also given.