Authors: | Stević, Stevo | Affiliations: | Mathematical Institute of the Serbian Academy of Sciences and Arts | Title: | Global stability of a max-type difference equation | Journal: | Applied Mathematics and Computation | Volume: | 216 | Issue: | 1 | First page: | 354 | Last page: | 356 | Issue Date: | 1-Mar-2010 | Rank: | M21 | ISSN: | 0096-3003 | DOI: | 10.1016/j.amc.2010.01.020 | Abstract: | We show that every positive solution to the difference equationxn = max fenced(frac(A1, xn - p1α1), frac(A2, xn - p2α2), ..., frac(Ak, xn - pkαk)), n ∈ N0,where pi, i = 1, ..., k are natural numbers such that 1 ≤ p1 < ⋯ < pk, k ∈ N, Ai > 0, αi ∈ (- 1, 1), i = 1, ..., k, converges to max1 ≤ i ≤ k fenced(Aifrac(1, αi + 1)). This result improves and complements the main result in our recent note: S. Stević, Global stability of a difference equation with maximum, Appl. Math. Comput. 210 (2009) 525-529, since it also considers the case when αi ∈ (- 1, 0], i{dotless} = 1, ..., k. |
Keywords: | Convergence | Max-type difference equation | Positive solution | Primary 39A11 | Publisher: | Elsevier |
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