Authors: | Stević, Stevo | Affiliations: | Mathematical Institute of the Serbian Academy of Sciences and Arts | Title: | Global stability of a difference equation with maximum | Journal: | Applied Mathematics and Computation | Volume: | 210 | Issue: | 2 | First page: | 525 | Last page: | 529 | Issue Date: | 15-Apr-2009 | Rank: | M21 | ISSN: | 0096-3003 | DOI: | 10.1016/j.amc.2009.01.050 | Abstract: | We prove that every positive solution to the difference equationxn = max fenced(frac(A1, xn - 1α1), frac(A2, xn - 2α2), ..., frac(Ak, xn - kαk)), n ∈ N0,where k ∈ N, Ai > 0, αi ∈ (0, 1), i = 1, ..., k, converges to the following quantity max fenced(A1frac(1, α1 + 1), ..., Akfrac(1, αk + 1)), confirming a quite recent conjecture of interest. We also prove another result on global convergence which concerns some cases when not all αi, i = 1, ..., k belong to the interval (0, 1). |
Keywords: | Convergence | Max-type difference equation | Positive solution | Publisher: | Elsevier |
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