## On a generalized difference system.(English)Zbl 0894.39001

Let $$\overline T = \{t_0,t_1,\ldots \}$$ denote the set of increasing time instances, and $$x: \overline T \to \mathbb R^n$$ with $$x(k)=(x^1,x^2,\ldots,x^n)(t_k)$$. Consider the difference system $x(k+1)=f_k(x(0),x(1),\ldots,x(k)), k \in \mathbb N = \{0,1,2,\ldots \} \tag{1}$ where $$f_k:\mathbb R^{n(k+1)} \to \mathbb R^n$$, with the dependence of $$f_k$$ at the time $$t_k$$ annotated in the subscript. The system (1) is very general and in particular includes the prototype equation $$x(k+1)=f(k,x(k))$$, equations with finite as well as infinite delays, equations of neutral type, and the discrete integral equations of Volterra type. The paper contains a survey of recent results for the above system obtained by the authors.

### MSC:

 39A10 Additive difference equations 39A11 Stability of difference equations (MSC2000) 39A12 Discrete version of topics in analysis
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### References:

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