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 ∫ab 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-Stieltjesintegral in terms of Riemann-Stieltjes sums are also pointed out.

Keywords

• Ostrowski's inequality
• Quadrature formula
• Riemann-Stieltjes integral