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

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Ukrainian Mathematical Journal Aims and scope

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.

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Authors and Affiliations

  1. Jerash University, Jerash, Jordan

    M. W. Alomari

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  1. M. W. Alomari
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Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 65, No. 7, pp. 894–916, July, 2013.

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Alomari, M.W. New Sharp Ostrowski-type Inequalities and Generalized Trapezoid-type Inequalities for Riemann–Stieltjes Integrals and their Applications. Ukr Math J 65, 995–1018 (2013). https://doi.org/10.1007/s11253-013-0837-z

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  • DOI: https://doi.org/10.1007/s11253-013-0837-z

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