On a Class of Difference Equations with Interlacing Indices of the Fourth Order

The following class of nonlinear difference equations of the fourth order x(n+1) = alpha x(n-1) + bx(n-1)x(n-3) /cx(n-1) + dx(n-3), n is an element of N-0, where the parameters a, b, c, d and the initial values x(- j), j = 0,3, are positive real numbers, has been considered recently in this journal. Here we give a detailed analysis of the results and claims given therein, give many explanations and remarks related to the results and claims, explain some problems with some of the claims by providing suitable counterexamples, compare the results therein with some previous results in the literature, and present a global convergence result.

Automated summary

This paper provides a detailed analysis of a class of nonlinear fourth-order difference equations. It studies the case where the parameters and initial values are positive real numbers and gives explanations and remarks related to the results and claims. It also addresses issues with some of the claims by providing counterexamples and compares the results with previous findings in the literature. Additionally, a global convergence result is presented.