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

Mohammad W. Alomari — 2016

Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica

A sharp companion of Ostrowski’s inequality for the Riemann-Stieltjes integral [...] ∫abf(t) du(t) a b f ( t ) d u ( 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.

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