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Explicit bounds for second-order difference equations and a solution to a question of Stević. (English) Zbl 1076.39004

The authors obtain explicit bounds for the solutions of the second order difference equation \[ b_i=(2+g(i-1))\, b_{i-1}-(1+h(i-1))\,b_{i-2} \quad\text{for }i \geq 2, \] and provide sharp inequalities for \(\{b_i\}\) in terms of the sequences \(\{g(i)\}\) and \(\{h(i)\}\), and the initial values \(b_0\) and \(b_1\).
The main result solves partially a question of S. Stević [ANZIAM J. 46, 157–170 (2004; Zbl 1061.39007)] concerning to the asymptotic behavior of the particular case of \(g(i)=c/i^2\) for some nonnegative constant \(c\).

MSC:

39A11 Stability of difference equations (MSC2000)

Citations:

Zbl 1061.39007
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References:

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