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2011/2012 Mean Value Integral Inequalities
Rodrigo López Pouso
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Real Anal. Exchange 37(2): 439-450 (2011/2012).


Let \(F:[a,b]\longrightarrow \R\) have zero derivative in a dense subset of \([a,b]\). What else we need to conclude that \(F\) is constant in \([a,b]\)? We prove a result in this direction using some new Mean Value Theorems for integrals which are the real core of this paper. These Mean Value Theorems are proven easily and concisely using Lebesgue integration, but we also provide alternative and elementary proofs to some of them which keep inside the scope of the Riemann integral.


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Rodrigo López Pouso. "Mean Value Integral Inequalities." Real Anal. Exchange 37 (2) 439 - 450, 2011/2012.


Published: 2011/2012
First available in Project Euclid: 15 April 2013

zbMATH: 1277.26016
MathSciNet: MR3080603

Primary: 26A42 , 26D15
Secondary: 97I50

Keywords: mean value theorem , Riemann integration

Rights: Copyright © 2011 Michigan State University Press

Vol.37 • No. 2 • 2011/2012
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