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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