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BY-NC-ND 3.0 license Open Access Published by De Gruyter Open Access June 6, 2014

Inequalities and Means from a Cyclic Differential Equation

  • Gerd Herzog EMAIL logo and Peer Chr. Kunstmann
From the journal Demonstratio Mathematica

Abstract

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.

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Received: 2013-1-23
Revised: 2013-4-29
Published Online: 2014-6-6
Published in Print: 2014-6-1

© 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.

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