Error bounds in approximating the Riemann-Stieltjes integral of Cn+1-class integrands and nonsmooth integrators

S. S. Dragomir; Charis Harley; E. Momoniat

doi:10.1016/j.amc.2014.10.022

Error bounds in approximating the Riemann-Stieltjes integral of Cⁿ⁺¹-class integrands and nonsmooth integrators

S. S. Dragomir
, Charis Harley
, E. Momoniat

Victoria University
University of the Witwatersrand

Research output: Contribution to journal › Article › peer-review

2 Citations (Scopus)

Abstract

In the present paper we investigate the problem of approximating the Riemann-Stieltjes integral ∫_a^b f(λ) du(λ) in the case when the integrand f is (n + 1)-time differentiable (n ≥ 0) and the derivative f⁽ⁿ⁺¹⁾ is continuous on [a, b], while the integrator u is Riemann integrable on a, b]. A priory error bounds for different classes of functions are provided.

Original language	English
Pages (from-to)	237-246
Number of pages	10
Journal	Applied Mathematics and Computation
Volume	249
DOIs	https://doi.org/10.1016/j.amc.2014.10.022
Publication status	Published - 15 Dec 2014
Externally published	Yes

Keywords

Integral inequalities
Quadrature rule
Riemann-Stieltjes integral

ASJC Scopus subject areas

Computational Mathematics
Applied Mathematics

Access to Document

10.1016/j.amc.2014.10.022

Cite this

@article{e722a12b0b854c09888bc4217526f138,

title = "Error bounds in approximating the Riemann-Stieltjes integral of Cn+1-class integrands and nonsmooth integrators",

abstract = "In the present paper we investigate the problem of approximating the Riemann-Stieltjes integral ∫ab f(λ) du(λ) in the case when the integrand f is (n + 1)-time differentiable (n ≥ 0) and the derivative f(n+1) is continuous on [a, b], while the integrator u is Riemann integrable on a, b]. A priory error bounds for different classes of functions are provided.",

keywords = "Integral inequalities, Quadrature rule, Riemann-Stieltjes integral",

author = "Dragomir, \{S. S.\} and Charis Harley and E. Momoniat",

year = "2014",

month = dec,

day = "15",

doi = "10.1016/j.amc.2014.10.022",

language = "English",

volume = "249",

pages = "237--246",

journal = "Applied Mathematics and Computation",

issn = "0096-3003",

publisher = "Elsevier Inc.",

}

TY - JOUR

T1 - Error bounds in approximating the Riemann-Stieltjes integral of Cn+1-class integrands and nonsmooth integrators

AU - Dragomir, S. S.

AU - Harley, Charis

AU - Momoniat, E.

PY - 2014/12/15

Y1 - 2014/12/15

N2 - In the present paper we investigate the problem of approximating the Riemann-Stieltjes integral ∫ab f(λ) du(λ) in the case when the integrand f is (n + 1)-time differentiable (n ≥ 0) and the derivative f(n+1) is continuous on [a, b], while the integrator u is Riemann integrable on a, b]. A priory error bounds for different classes of functions are provided.

AB - In the present paper we investigate the problem of approximating the Riemann-Stieltjes integral ∫ab f(λ) du(λ) in the case when the integrand f is (n + 1)-time differentiable (n ≥ 0) and the derivative f(n+1) is continuous on [a, b], while the integrator u is Riemann integrable on a, b]. A priory error bounds for different classes of functions are provided.

KW - Integral inequalities

KW - Quadrature rule

KW - Riemann-Stieltjes integral

UR - https://www.scopus.com/pages/publications/84909606782

U2 - 10.1016/j.amc.2014.10.022

DO - 10.1016/j.amc.2014.10.022

M3 - Article

AN - SCOPUS:84909606782

SN - 0096-3003

VL - 249

SP - 237

EP - 246

JO - Applied Mathematics and Computation

JF - Applied Mathematics and Computation

ER -