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 ∫ab f(λ) du(λ) in the case when the integrand f is n-time differentiable and the derivative f(n) is either of locally bounded variation, or Lipschitzian on an interval incorporating [a, b]. 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. © 2013 Dragomir and Abelman; licensee Springer.