A sharp companion of Ostrowski’s inequality for the Riemann–Stieltjes integral and applications

Abstract

A sharp companion of Ostrowski’s inequality for the Riemann-Stieltjes integral $∫_a^b f(t) du(t)$, where $f$ is assumed to be of $r-H-Hölder$ type on $[a, b]$ and $u$ is of bounded variation on $[a, b]$, is proved. Applications to the approximation problem of the Riemann-Stieltjes integral in terms of Riemann-Stieltjes sums are also pointed out.