Contracting invariant intervals and convergence properties of difference equations

Abstract

In this paper, we consider kth order difference equations of the form

where every function is continuous and monotonic in each of its arguments. We generalize and improve upon some previous techniques to prove convergence using invariant intervals as the common theme. We apply our techniques to several different special cases of the equation above.

Keywords:

• difference equations
• invariant intervals
• convergence properties
• kth order equations