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 ∫abf(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. © 2011 Elsevier Ltd.