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Ukrainian Mathematical Journal

, Volume 65, Issue 7, pp 995–1018 | Cite as

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

  • M. W. Alomari
Article

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.

Keywords

Bounded Variation Type Inequality Quadrature Rule Integral Inequality Stieltjes Integral 
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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  • M. W. Alomari
    • 1
  1. 1.Jerash UniversityJerashJordan

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