Approximating the Riemann-Stieltjes integral by a trapezoidal quadrature rule with applications

Abstract. In this paper we provide sharp bounds for the error in approximating the Riemann-Stieltjes integral R b a f (t) du (t) by the trapezoidal rule f (a) + f (b) 2 [u (b) u (a)] under various assumptions for the integrand f and the integrator u for which the above integral exists. Applications for continuous functions of selfadjoint operators in Hilbert spaces are provided as well.

• Type: Journal
• Year: 2011
• Where: MCM
• Authors: S. S. Dragomir
• Keywords: Communications, Hilbert Spaces, Integrand, MCM 2011, Selfadjoint Operators