A Companion of Ostrowski inequality for the Stieltjes integral of monotonic functions

Some companions of Ostrowski’s integral inequality for the RiemannStieltjes integral \int_a^b{ f (t) du (t)}, where f is assumed to be of r-H-H¨older type on [a, b] and u is of monotonic non-decreasing on [a, b], are proved. Applications to the approximation problem of the Riemann-Stieltjes integral in terms of Riemann-Stieltjes sums are also pointed out.