Authors: Stević, Stevo 
Affiliations: Mathematical Institute of the Serbian Academy of Sciences and Arts 
Title: On the difference equation xn + 1 = α + frac(xn - 1, xn)
Journal: Computers and Mathematics with Applications
Volume: 56
Issue: 5
First page: 1159
Last page: 1171
Issue Date: 1-Sep-2008
Rank: M22
ISSN: 0898-1221
DOI: 10.1016/j.camwa.2008.02.017
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].
Keywords: Asymptotics | Convergence to zero | Difference equation | Inclusion theorem | Period three solution
Publisher: Elsevier

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