A sharp companion of Ostrowski’s inequality for the Riemann–Stieltjes integral and applications

Alomari, Mohammad W.

doi:10.1515/aupcsm-2016-0006

Abstract

A sharp companion of Ostrowski’s inequality for the Riemann-Stieltjes integral $\int_{a}^{b} f (t) du (t)$ $\int_a^b {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-Stieltjes integral in terms of Riemann-Stieltjes sums are also pointed out.

References

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A sharp companion of Ostrowski’s inequality for the Riemann–Stieltjes integral and applications

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