ON THE OSTROWSKI INEQUALITY FOR THE RIEMANN-STIELTJES INTEGRAL ${\int}_a^b$ f (t) du (t), WHERE f IS OF HÖLDER TYPE AND u IS OF BOUNDED VARIATION AND APPLICATIONS

In this paper we point out an Ostrowski type inequality for the Riemann-Stieltjes integral ${\int}_a^b$ f (t) du (t), where f is of p-H-$H{\ddot{o}}lder$ type on [a,b], and u is of bounded variation on [a,b]. Applications for the approximation problem of the Riemann-Stieltjes integral in terms of Riemann-Stieltjes sums are also given.