2017
Том 69
№ 9

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New Sharp Ostrowski-type Inequalities and Generalized Trapezoid-type Inequalities for Riemann–Stieltjes Integrals and their Applications

Alomari M. W.

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Abstract

We prove new sharp weighted generalizations of Ostrowski-type and generalized trapezoid-type inequalities for Riemann–Stieltjes integrals. Several related inequalities are deduced and investigated. New Simpson-type inequalities are obtained for the \( \mathcal{R}\mathcal{S} \) -integral. Finally, as an application, we estimate the error of a general quadrature rule for the \( \mathcal{R}\mathcal{S} \) -integral via the Ostrowski–generalized-trapezoid-quadrature formula.

English version (Springer): Ukrainian Mathematical Journal 65 (2013), no. 7, pp 995-1018.

Citation Example: Alomari M. W. New Sharp Ostrowski-type Inequalities and Generalized Trapezoid-type Inequalities for Riemann–Stieltjes Integrals and their Applications // Ukr. Mat. Zh. - 2013. - 65, № 7. - pp. 894–916.

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