On Simpson's inequality and applications
type: Item
instance of: scholarly article
title: On Simpson's inequality and applications
zbMATH Open document ID: 0976.26012
DOI: 10.1155/S102558340000031X
author: Silvestru Sever Dragomir
author: Ravi P. Agarwal
author: P. Cerone
published in: Journal of Inequalities and Applications
publication date: 2002-01-06T00:00:00Z
full work available at URL: https://eudml.org/doc/121437
review text: This is a survey paper on recent developments on Simpson's inequality, Simpson's quadrature formula and various related results. The following theorem is typical: Let \(f: [a,b]\to\mathbb{R}\) be of bounded variation on \([a,b]\). Then \[ \Biggl|\int^b_a f(x) dx- {b-a\over 6} \Biggl[ f(a)+ 4f\Biggl({a+ b\over 2}\Biggr)+ f(b)\Biggr]\Biggr|\leq {1\over 3} (b-a) \bigvee^b_a (f), \] where \(\bigvee^b_a(f)\) is the total variation of \(f\) on \([a,b]\). Except two of the 38 cited papers, all are due to Dragomir et al. Each chapter in this paper is concluded with certain applications of the results for special means of two arguments. It is not mentioned that the first application to special means of Simpson's quadrature formula is due to the reviewer [Arch. Math. 56, No. 5, 471-473 (1991; Zbl 0693.26005); see also Aequationes Math. 40, No. 2/3, 261-270 (1990; Zbl 0717.26014)].
reviewed by: József Sándor
Mathematics Subject Classification ID: 26D15
Mathematics Subject Classification ID: 26D20
Mathematics Subject Classification ID: 41A55
Mathematics Subject Classification ID: 65D32
zbMATH DE Number: 1563279
zbMATH Keywords: Simpson's inequality
zbMATH Keywords: Simpson's quadrature formula
zbMATH Keywords: total variation
zbMATH Keywords: special means
MaRDI profile type: Publication
OpenAlex ID: W2084967964
description: scientific article; zbMATH DE number 1563279