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

作者：Dragomir S S^*; Abelman S

来源：Journal of Inequalities and Applications, 2013, 2013(1): 154.

DOI：10.1186/1029-242X-2013-154

• Riemann-Stieltjes integral
• Taylor%26apos
• s representation
• functions of bounded variation
• Lipschitzian functions
• integral transforms
• finite Laplace-Stieltjes transform
• finite Fourier-Stieltjes sine and cosine transforms

In the present paper, we investigate the problem of approximating the Riemann-Stieltjes integral integral(b)(a) f(lambda) du(lambda) 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.

• 出版日期2013