On the difference equation xn + 1 = α + frac(xn - 1, xn)

Abstract

In this paper we study the behavior of the solutions of the difference equation xn + 1 = α + frac(xn - 1, xn), n = 0, 1, ... where α is a negative number. Included are results which considerably improve and correct those in the recently published paper: [A.E. Hamza, On the recursive sequence xn + 1 = α + frac(xn - 1, xn), J. Math. Anal. Appl. 322 (2006), 668-674]. We also refute Conjecture 2 in [G. Ladas, Open problems and conjectures, J. Difference. Equ. Appl. 7 (2) (2001), 477-482].