Authors: | Stević, Stevo | Affiliations: | Mathematical Institute of the Serbian Academy of Sciences and Arts | Title: | On the recursive sequence xn + 1 = max {c, frac(xnp, xn - 1p)} | Journal: | Applied Mathematics Letters | Volume: | 21 | Issue: | 8 | First page: | 791 | Last page: | 796 | Issue Date: | 1-Aug-2008 | Rank: | M22 | ISSN: | 0893-9659 | DOI: | 10.1016/j.aml.2007.08.008 | Abstract: | This work studies the boundedness and global attractivity for the positive solutions of the difference equation xn + 1 = max {c, frac(underover(x, n, p), underover(x, n - 1, p))}, n ∈ N0, with p, c ∈ (0, ∞). It is shown that: (a) there exist unbounded solutions whenever p ≥ 4, (b) all positive solutions are bounded when p ∈ (0, 4), (c) every positive solution is eventually equal to 1 when p ∈ (0, 4) and c ≥ 1, (d) all positive solutions converge to 1 whenever p, c ∈ (0, 1). |
Keywords: | Boundedness | Difference equation | Global attractivity | Max type difference equations | Publisher: | Elsevier |
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