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

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

Moroccan Journal of Pure and Applied Analysis

Volume 4 (2018): Issue 2 (December 2018)

By: M.W. Alomari

Open Access

|May 2019

Abstract

In this work, we construct a new general two-point quadrature rules for the Riemann–Stieltjes integral $\int_{a}^{b} f (t) d u (t)$ $\int_a^b {f(t)} \,du\,(t)$, 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 L^p–Error estimates for the proposed quadrature rules are also obtained.

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Articles in this issue

DOI: https://doi.org/10.1515/mjpaa-2018-0010 | Journal eISSN: 2351-8227

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Language: English

Page range: 94 - 109

Submitted on: Jan 2, 2019

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Accepted on: Apr 3, 2019

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Published on: May 16, 2019

Published by: Sciendo

In partnership with: Paradigm Publishing Services

Publication frequency: 3 issues per year

Keywords:

Quadrature formula,

Riemann-Stieltjes integral,

Ostrowski’s inequality

Related subjects:

Differential equations and dynamical systems,

Probability and statistics,

Numerical and computational mathematics

© 2019 M.W. Alomari, published by Sciendo
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

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