Fixed points of order-reversing maps in ℝ and chemical equilibrium

✍ Scribed by Gilles Gnacadja

• Publisher: John Wiley and Sons
• Year: 2006
• Tongue: English
• Weight: 134 KB
• Volume: 30
• Category: Article
• ISSN: 0170-4214
• DOI: 10.1002/mma.782

✦ Synopsis

Abstract

The problem of computing the equilibrium state of a reversible chemical reaction network has a natural interpretation as a fixed‐point problem. Several authors have used fixed‐point iterations in this context, yet there are no comprehensive investigations into the convergence of the algorithm. We address this void by studying the larger problem of the existence and uniqueness of fixed points, and the convergence of fixed‐point iterations, for order‐reversing maps in ℝ. By using the Thompson metric, we are able to apply fixed‐point theorems based on the Lipschitz condition and obtain upper bounds on judiciously defined approximation errors. Copyright © 2006 John Wiley & Sons, Ltd.