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.
✦ LIBER ✦
New Sharp Ostrowski-type Inequalities and Generalized Trapezoid-type Inequalities for Riemann–Stieltjes Integrals and their Applications
✍ Scribed by Alomari, M. W.
- Book ID
- 121585035
- Publisher
- Springer
- Year
- 2013
- Tongue
- English
- Weight
- 175 KB
- Volume
- 65
- Category
- Article
- ISSN
- 0041-5995
No coin nor oath required. For personal study only.
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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.