Geodesic
A sharp companion of Ostrowski’s inequality for the Riemann–Stieltjes integral and applications
Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica, no. 15 (2016).

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A sharp companion of Ostrowski’s inequality for the Riemann-Stieltjes integral [...] ∫abf(t) du(t) ∫_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.
Keywords: Ostrowski’s inequality, Quadrature formula, Riemann-Stieltjes integral 
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Alomari, Mohammad W. A sharp companion of Ostrowski’s inequality for the Riemann–Stieltjes integral and applications. Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica, no. 15 (2016). http://geodesic.mathdoc.fr/item/AUPCM_2016_15_a0/