A generalization of general two-point formula with applications in numerical integration

Kovač, Sanja; Pečarić, Josip; Vukelić, Ana

doi:10.1016/j.na.2007.01.069

Cited by 8 publications

(3 citation statements)

References 5 publications

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“…A general two-point integral quadrature formula, using the concept of harmonic polynomials, was derived in [22].…”

Section: Symmetric Inequality Of Guessab and Schmeisser [18]mentioning

confidence: 99%

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Ostrowski type inequalities and some selected quadrature formulae

Milovanović

2021

Appl Anal Discrete Math

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Some selected Ostrowski type inequalities and a connection with numerical integration are studied in this survey paper, which is dedicated to the memory of Professor D. S. Mitrinovic, who left us 25 years ago. His significant inuence to the development of the theory of inequalities is briefly given in the first section of this paper. Beside some basic facts on quadrature formulas and an approach for estimating the error term using Ostrowski type inequalities and Peano kernel techniques, we give several examples of selected quadrature formulas and the corresponding inequalities, including the basic Ostrowski's inequality (1938), inequality of Milovanovic and Pecaric (1976) and its modifications, inequality of Dragomir, Cerone and Roumeliotis (2000), symmetric inequality of Guessab and Schmeisser (2002) and asymmetric in-equality of Franjic (2009), as well as four point symmetric inequalites by Alomari (2012) and a variant with double internal nodes given by Liu and Park (2017).

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“…A general two-point integral quadrature formula, using the concept of harmonic polynomials, was derived in [22].…”

Section: Symmetric Inequality Of Guessab and Schmeisser [18]mentioning

confidence: 99%

“…Inspired by (22), Alomari [2] considered the following symmetric rule 4,0 (f ). We suppose that λ ∈ (0, 1) in order to have positive weight coefficients, as well as 0 ≤ x ≤ 1.…”

Section: Four Point Symmetric Inequality Of Alomari [2]mentioning

confidence: 99%

Ostrowski type inequalities and some selected quadrature formulae

Milovanović

2021

Appl Anal Discrete Math

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show abstract

“…A number of error estimates for the identity (1.4) are obtained, and various examples of the general two-point quadrature formula are given in [3]. The goal of this paper is to establish analogous formula for the weighted case, i.e.…”

Section: 3)mentioning

confidence: 99%