Approximating the Riemann-Stieltjes integral of smooth integrands and of bounded variation integrators

Abstract 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 seve...
Ausführliche Beschreibung

Abstract 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. Ausführliche Beschreibung