Inequalities and Means from a Cyclic Differential Equation
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.
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
De Gruyter
2014-06-01
|
| Series: | Demonstratio Mathematica |
| Subjects: | |
| Online Access: | http://www.degruyter.com/view/j/dema.2014.47.issue-2/dema-2014-0024/dema-2014-0024.xml?format=INT |