Comparing two integral means for absolutely continuous mappings whose derivatives are in \(L_\infty[a,b]\) and applications
type: Item
instance of: scholarly article
title: Comparing two integral means for absolutely continuous mappings whose derivatives are in \(L_\infty[a,b]\) and applications
zbMATH Open document ID: 1014.26016
DOI: 10.1016/S0898-1221(02)00144-X
author: N. S. Barnett
author: A. M. Fink
author: P. Cerone
author: Silvestru Sever Dragomir
publication date: 2002-08-15T00:00:00Z
review text: Let \(f:[a,b]\rightarrow \mathbb{R}\) be an absolutely continuous mapping with \( f^{\prime }\in L_{\infty }[a,b]\) , i. e. \(\left\|f^{\prime }\right\|_{\infty }=ess \sup_{t\in [a,b]}\left|f^{\prime }(t)\right|<\infty .\) The authors prove that for \([c,d]\subset [a,b]\) is valid the following estimate: \[ \left|\frac{1}{b-a}\int_{a}^{b}f(t)dt-\frac{1}{d-c}\int_{c}^{d}f(t)dt \right|\leq \frac{1}{2}[(b-a)-(d-c)]\left\|f^{\prime }\right\|_{\infty }. \] This is a generalization of the classical Ostrowski inequality which may be deduced for \(c=x\in \left( a,b\right) \) and \(d\rightarrow x\) . Applications for probability density functions, special means, Jeffreys' divergence and continuous streams are given.
Mathematics Subject Classification ID: 26D15
Mathematics Subject Classification ID: 60E05
Mathematics Subject Classification ID: 62E10
zbMATH DE Number: 1781566
zbMATH Keywords: Ostrowski's inequality
zbMATH Keywords: integral means
zbMATH Keywords: probability density function
zbMATH Keywords: Jeffreys divergence
zbMATH Keywords: continuous streams
reviewed by: Gheorghe Toader
MaRDI profile type: Publication
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full work available at URL: s0898-1221(02)00144-x
OpenAlex ID: W1975418190
published in: Computers & Mathematics with Applications
description: scientific article; zbMATH DE number 1781566