Authors: Berenhaut, Kenneth
Foley, John
Stević, Stevo 
Affiliations: Mathematical Institute of the Serbian Academy of Sciences and Arts 
Title: Quantitative bounds for the recursive sequence yn + 1 = A + frac(yn, yn - k)
Journal: Applied Mathematics Letters
Volume: 19
Issue: 9
First page: 983
Last page: 989
Issue Date: 1-Sep-2006
Rank: M23
ISSN: 0893-9659
DOI: 10.1016/j.aml.2005.09.009
Abstract: 
This note provides new quantitative bounds for the recursive equation yn + 1 = A + frac(yn, yn - k), n = 0, 1, ..., where y- k, y- k + 1, ..., y- 1, y0, A ∈ (0, ∞) and k ∈ {2, 3, 4, ...}. Issues regarding exponential convergence of solutions are also considered. In particular, it is shown that exponential convergence holds for all (A, k) for which global asymptotic stability was proven in [R.M. Abu-Saris, R. DeVault, Global stability of yn + 1 = A + frac(yn, yn - k), Appl. Math. Lett. 16 (2) (2003) 173-178].
Keywords: Difference equation | Explicit bounds | Exponential convergence | Stability
Publisher: Elsevier

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