Mappings with a single critical point and applications to rational difference equations

Abstract

Convergence properties of first-order difference equations of the form are established for a general class of mappings f, where f has at most one critical point. Using these results, we find necessary and sufficient conditions for the convergence of the solutions for all difference equations of the form

for all possible choices of non-negative coefficients and positive initial values.

Keywords::

• first-order map
• rational difference equations
• convergence
• single critical point