Sharp error bounds in approximating the Riemann-Stieltjes integral by a generalised trapezoid formula and applications

Abstract

Sharp error bounds in approximating the Riemann-Stieltjes integral f ba f(t) du(t) with the generalised trapezoid formula f (b)[u(b)-1/b-a fba u(s) ds] + f (a)[1/b-a fba u(s) ds - u(a)] are given for various pairs (f, u) of functions. Applications for weighted integrals are also provided. © 2013 Cerone and Dragomir.