On the global behavior of higher order recursive sequences.

*(English)*Zbl 1127.39016Summary: 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.

##### MSC:

39A11 | Stability of difference equations (MSC2000) |

##### Keywords:

difference equations; linearized equation; local stability; global attractivity; global stability
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\textit{M. Jaberi Douraki} et al., Appl. Math. Comput. 169, No. 2, 819--831 (2005; Zbl 1127.39016)

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