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On the global behavior of higher order recursive sequences. (English) Zbl 1127.39016
Summary: Our basic purpose in this paper is to establish some conditions for the global attractivity and convergence of the \(k\)th-order recursive sequence \[ x_n=f(x_{n-1},x_{n-2},\dots,x_{n-k}),\;n=1,2,3,\dots \] We will show that if \(f\) is a real-valued function with a convex basin \(\Omega\) in \(R^k\), which is differentiable with bounded differential, then \(f\) has an equilibrium point. Our final comments are about informative examples.

39A11 Stability of difference equations (MSC2000)
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