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Demonstratio Mathematica

Editor-in-Chief: Vetro, Calogero

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Volume 47, Issue 2


Inequalities and Means from a Cyclic Differential Equation

Gerd Herzog / Peer Chr. Kunstmann
Published Online: 2014-06-06 | DOI: https://doi.org/10.2478/dema-2014-0024


We prove that the solution of the cyclic initial value problem u’k = 1/2 - uk/(uk+1 + uk+2) (k Z/nZ), u(0)= x is convergent to an equilibrium μ (x) (1,…,1), and study the properties of the function x → μ(x) and its relation to Shapiro’s inequality.

Keywords: Shapiro inequality; cyclic differential equation; quasimonotonicity


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About the article

Received: 2013-01-23

Revised: 2013-04-29

Published Online: 2014-06-06

Published in Print: 2014-06-01

Citation Information: Demonstratio Mathematica, Volume 47, Issue 2, Pages 300–309, ISSN (Online) 2391-4661, ISSN (Print) 0420-1213, DOI: https://doi.org/10.2478/dema-2014-0024.

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© by Gerd Herzog. This article is distributed under the terms of the Creative Commons Attribution Non-Commercial License, which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited. BY-NC-ND 3.0

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