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Global asymptotic stability of a family of difference equations. (English) Zbl 1172.39018

For the difference equation

x n =[(f 1 f 2 f 3 +f 1 +f 2 +f 3 +h)/(f 1 f 2 +f 1 f 3 +f 2 f 3 +g+h)](x n-1 ,,x n-r )

with continuous functions f 1 ,f 2 ,f 3 ,g,h:( + ) r + and positive initial values, sufficient conditions are given such that 1 is a globally asymptotic stable equilibrium.

MSC:
39A11Stability of difference equations (MSC2000)
39A20Generalized difference equations
References:
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