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2016•Annales Universitatis Paedagogicae Cracoviensis Studia MathematicaOpen access

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

Mohammad W. Alomari

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Abstract

Abstract A sharp companion of Ostrowski’s inequality for the Riemann-Stieltjes integral $\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.

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Abstract A sharp companion of Ostrowski’s inequality for the Riemann-Stieltjes integral $\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.

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Available abstract

Abstract A sharp companion of Ostrowski’s inequality for the Riemann-Stieltjes integral $\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.

Key concepts: Riemann–Stieltjes integral, Mathematics, Riemann integral, Daniell integral, Riemann hypothesis, Bounded function, Pure mathematics, Bounded variation

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