The nonlinear rational difference equations are of paramount importance in their own right, and furthermore for the development of the basic theory of the global behavior of nonlinear difference equations. The authors study the global attractivity of the rational recursive sequence
where or equal are real numbers and or equal 1 is an integer, and the initial conditions and are arbitrary. They prove that the positive equilibrium of equation (1) is a global attractor with a basin that depends on certain conditions of the coefficients.
I think that the authors must be aware of relevant published papers on the same topic, for example W. A. Kosmala, M. R. S. Kulenovic, G. Ladas and C. T. Teixeira [J. Math. Anal. Appl. 251, No. 2, 571-586 (2000; Zbl 0967.39004)].