A sharp companion of Ostrowski's inequality for the Riemann-Stieltjes integral and applications

Mohammad W. Alomari

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

Mathematics Subject Classification (2010)


26D15; 26D20; 41A55

References


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