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

Abstract

The following class of nonlinear difference equations of the fourth order xn+1=axn−1+bxn−1xn−3cxn−1+dxn−3,n∈N0, 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.