Approximating the Riemann-Stieltjes integral of smooth integrands and of bounded variation integrators
1 School of Computational & Applied Mathematics, University of the Witwatersrand, Private Bag-3, Wits-2050, Johannesburg, South Africa
2 Mathematics, College of Engineering & Science, Victoria University, P.O. Box 14428, Melbourne, MC 8001, Australia
Journal of Inequalities and Applications 2013, 2013:154 doi:10.1186/1029-242X-2013-154Published: 4 April 2013
In the present paper, we investigate the problem of approximating the Riemann-Stieltjes integral in the case when the integrand f is n-time differentiable and the derivative is either of locally bounded variation, or Lipschitzian on an interval incorporating . A priory error bounds for several classes of integrators u and applications in approximating the finite Laplace-Stieltjes transform and the finite Fourier-Stieltjes sine and cosine transforms are provided as well.
MSC: 41A51, 26D15, 26D10.