A companion of Ostrowski’s inequality for the Riemann–Stieltjes integral ∫abf(t)du(t), where f is of bounded variation and u is of r-H-Hölder type and applications

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