Jump to ContentJump to Main Navigation
Show Summary Details
More options …

Demonstratio Mathematica

Editor-in-Chief: Vetro, Calogero


Covered by:
Web of Science - Emerging Sources Citation Index
Scopus
MathSciNet


CiteScore 2017: 0.28
SCImago Journal Rank (SJR) 2017: 0.231
Source Normalized Impact per Paper (SNIP) 2017: 0.443
Mathematical Citation Quotient (MCQ) 2017: 0.12
ICV 2017: 121.78



Open Access
Online
ISSN
2391-4661
See all formats and pricing
More options …
Volume 47, Issue 2

Issues

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

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.

Keywords: Shapiro inequality; cyclic differential equation; quasimonotonicity

References

  • [1] P. S. Bullen, A Dictionary of Inequalities, Harlow: Longman, (1998).Google Scholar

  • [2] V. Cîrtoaje, Solution of Problem 3195, Crux Mathematicorum 33 (2007), 496-499. Google Scholar

  • [3] A. Clausing, A review of Shapiro’s cyclic inequality, General inequalities 6, Proc. 6th Int. Conf., Oberwolfach/Ger. 1990, 17-31, (1992).Google Scholar

  • [4] P. Hartman, Ordinary Differential Equations, Philadelphia, PA: SIAM, (2002).Google Scholar

  • [5] D. S. Mitrinovic, J. E. Pecaric, A. M. Fink, Classical and New Inequalities in Analysis, Dordrecht, Kluwer Academic Publishers, (1993).Google Scholar

  • [6] S. H. Shapiro, Advanced problem 4603, Amer. Math. Monthly 61 (1954), 571.Google Scholar

  • [7] P. Volkmann, Über die Invarianz konvexer Mengen und Differentialungleichungen in einem normierten Raume, Math. Ann. 203 (1973), 201-210.Google Scholar

  • [8] W. Walter, Differential and Integral Inequalities, Berlin-Heidelberg-New York, Springer- Verlag, (1970). Google Scholar

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.

Export Citation

© 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

Comments (0)

Please log in or register to comment.
Log in