Majorisation inequalities for Stieltjes integrals
β Scribed by N.S. Barnett; P. Cerone; S.S. Dragomir
- Publisher
- Elsevier Science
- Year
- 2009
- Tongue
- English
- Weight
- 400 KB
- Volume
- 22
- Category
- Article
- ISSN
- 0893-9659
No coin nor oath required. For personal study only.
β¦ Synopsis
Inequalities of the majorisation type for convex functions and Stieltjes integrals are given. Applications for some particular convex functions of interest are also presented.
π SIMILAR VOLUMES
Some Ostrowski and trapezoid type inequalities for the Stieltjes integral in the case of Lipschitzian integrators for both HΓΆlder continuous and monotonic integrals are obtained. The dual case is also analysed. Applications for the midpoint rule are pointed out as well.
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.
We derive a number of inequalities which must be satisfied by the interelectron repulsion integrals occurring in quantum mechanical calculations. These inequalities are valid for any type of basis functions or orbitals. They can be useful in testing computer programs which evaluate these integrals.