<abstract xmlns="http://www.w3.org/1999/xhtml">In this work, we construct a new general two-point quadrature rules for the Riemann–Stieltjes integral <inline-formula><alternatives><inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/j_mjpaa-2018-0010_eq_001.png"></inline-graphic><math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mrow><mrow><msubsup><mo>∫</mo><mi>a</mi><mi>b</mi></msubsup><mrow><mi>f</mi><mo>(</mo><mi>t</mi><mo>)</mo></mrow></mrow><mi> </mi><mi>d</mi><mi>u</mi><mi> </mi><mo>(</mo><mi>t</mi><mo>)</mo></mrow></math><tex-math>$\int_a^b {f(t)} \,du\,(t)$</tex-math></alternatives></inline-formula>, where the integrand <italic>f</italic> is assumed to be satisfied with the Hölder condition on [<italic>a</italic>, <italic>b</italic>] and the integrator <italic>u</italic> is of bounded variation on [<italic>a</italic>, <italic>b</italic>]. The dual formulas under the same assumption are proved. Some sharp error <italic>Lp</italic>–Error estimates for the proposed quadrature rules are also obtained.</abstract>

In this work, we construct a new general two-point quadrature rules for the Riemann–Stieltjes integral ∫abf(t) du (t)$\int_a^b {f(t)} \,du\,(t)$, where the integrand f is assumed to be satisfied with the Hölder condition on [a, b] and the integrator u is of bounded variation on [a, b]. The dual formulas under the same assumption are proved. Some sharp error Lp–Error estimates for the proposed quadrature rules are also obtained.

Two-Point Quadrature Rules for Riemann–Stieltjes Integrals with <italic>Lp</italic>–error estimates

Department of Mathematics, Faculty of Science and Information Technology

Moroccan Journal of Pure and Applied Analysis

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Two-Point Quadrature Rules for Riemann–Stieltjes Integrals with –error estimates

In this work, we construct a new general two-point quadrature rules for the Riemann–Stieltjes integral ∫abf(t) du (t)$\int_a^b {f(t)} \,du\,(t)$, where the...

Two-Point Quadrature Rules for Riemann–Stieltjes Integrals with L^p–error estimates

Published Online: May 16, 2019

Page range: 94 - 109

Received: Jan 02, 2019

Accepted: Apr 03, 2019

DOI: https://doi.org/10.1515/mjpaa-2018-0010

Keywords
Quadrature formula, Riemann-Stieltjes integral, Ostrowski’s inequality

© 2018 M.W. Alomari, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Two-Point Quadrature Rules for Riemann–Stieltjes Integrals with Lp–error estimates

Published Online: May 16, 2019

Page range: 94 - 109

Received: Jan 02, 2019

Accepted: Apr 03, 2019

DOI: https://doi.org/10.1515/mjpaa-2018-0010

KeywordsQuadrature formula, Riemann-Stieltjes integral, Ostrowski’s inequality

© 2018 M.W. Alomari, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Two-Point Quadrature Rules for Riemann–Stieltjes Integrals with L^p–error estimates

Keywords
Quadrature formula, Riemann-Stieltjes integral, Ostrowski’s inequality