Sequences of maps and convergence properties of first-order difference equations with variable coefficients - Huang, Ying Sue; Knopf, Peter M. (Journal of difference equations and applications, 2017)
We consider sequences of continuous functions on that converge to a continuous monotone limit function. We prove a convergence theorem for the iterative map This result is used to solve an open problem in the field concerning the convergence properties of first-order rational difference equations that are linear in numerator and denominator with variable coefficients. We also establish convergence properties for a certain class of systems of first-order difference equations.