<i>L<sup>p</sup></i>–Error Bounds of Two and Three–Point Quadrature Rules For Riemann–Stieltjes Integrals

Alomari, Mohammad W.; Guessab, Allal

doi:10.1515/mjpaa-2018-0004

Cited by 3 publications

(3 citation statements)

References 19 publications

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“…which gives the desired result (14). The proof of the second inequality in (15) follows similarly by considering l = 2ν (ν ≥ 1) and omitting the details.…”

Section: Other Estimations Involving Normsmentioning

confidence: 70%

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A Perturbed Milne’s Quadrature Rule for n-Times Differentiable Functions with Lp-Error Estimates

Hazaymeh,

Saadeh,

Hatamleh

et al. 2023

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In this work, a perturbed Milne’s quadrature rule for n-times differentiable functions with Lp-error estimates is derived. One of the most important advantages of our result is that it is verified for p-variation and Lipschitz functions. Several error estimates involving Lp-bounds are proven. These estimates are useful if the fourth derivative is unbounded in L∞-norm or the Lp-error estimate is less than the L∞-error estimate. Furthermore, since the classical Milne’s quadrature rule cannot be applied either when the fourth derivative is unbounded or does not exist, the proposed quadrature could be used alternatively. Numerical experiments showing that our proposed quadrature rule is better than the classical Milne rule for certain types of functions are also provided. The numerical experiments compare the accuracy of the proposed quadrature rule to the classical Milne rule when approximating different types of functions. The results show that, for certain types of functions, the proposed quadrature rule is more accurate than the classical Milne rule.

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“…which gives the desired result (14). The proof of the second inequality in (15) follows similarly by considering l = 2ν (ν ≥ 1) and omitting the details.…”

Section: Other Estimations Involving Normsmentioning

confidence: 70%

“…Remark 1. Clearly, the estimation in (14) improves the first estimation in (13) by 1 2 when m is odd and thus (14) is better than (13).…”

Section: Other Estimations Involving Normsmentioning

confidence: 89%

A Perturbed Milne’s Quadrature Rule for n-Times Differentiable Functions with Lp-Error Estimates

Hazaymeh,

Saadeh,

Hatamleh

et al. 2023

Axioms

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“…For other related results see [6]. For different approaches variant quadrature formulae the reader may refer to [1], [8], [21] and [28].…”

Section: Introductionmentioning

confidence: 99%

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

Alomari

2018

Moroccan Journal of Pure and Applied Analysis

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Sharp inequality of three point Gauss—Legendre quadrature rule

Kashuri¹

2020

Proyecciones (Antofagasta)

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L^p–Error Bounds of Two and Three–Point Quadrature Rules For Riemann–Stieltjes Integrals

Abstract: In this work, L p -error estimates of general two and three point quadrature rules for Riemann-Stieltjes integrals are given. The presented proofs depend on new triangle type inequalities of Riemann-Stieltjes integrals.

Cited by 3 publications

References 19 publications

A Perturbed Milne’s Quadrature Rule for n-Times Differentiable Functions with Lp-Error Estimates

A Perturbed Milne’s Quadrature Rule for n-Times Differentiable Functions with Lp-Error Estimates

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

Sharp inequality of three point Gauss—Legendre quadrature rule

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Lp–Error Bounds of Two and Three–Point Quadrature Rules For Riemann–Stieltjes Integrals

Abstract: In this work, L p -error estimates of general two and three point quadrature rules for Riemann-Stieltjes integrals are given. The presented proofs depend on new triangle type inequalities of Riemann-Stieltjes integrals.

Cited by 3 publications

References 19 publications

A Perturbed Milne’s Quadrature Rule for n-Times Differentiable Functions with Lp-Error Estimates

A Perturbed Milne’s Quadrature Rule for n-Times Differentiable Functions with Lp-Error Estimates

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

Sharp inequality of three point Gauss—Legendre quadrature rule

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L^p–Error Bounds of Two and Three–Point Quadrature Rules For Riemann–Stieltjes Integrals

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