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The global attractivity of the rational difference equation $y_{n}=1+\frac{y_{n-k}}{y_{n-m}}$

2007
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Proceedings of the American Mathematical Society
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This paper studies the behavior of positive solutions of the recursive equation with y −s , y −s+1 , . . . , y −1 ∈ (0, ∞) and k, m ∈ {1, 2, 3, 4, . . .}, where s = max{k, m}. We prove that if gcd(k, m) = 1, with k odd, then y n tends to 2, exponentially. When combined with a recent result of E.

doi:10.1090/s0002-9939-06-08580-7
fatcat:fs5jxfvgjzb45bkeyc2czed6oi