## Global attractivity in a rational recursive sequence.(English)Zbl 1019.39007

For the recursive sequence $$x_{n+1}= (\alpha-\beta x_n)/(\gamma+ x_{n-k})$$ with non-negative $$\alpha,\beta, \gamma$$ and natural $$k$$ it is shown that, under certain assumptions, the non-negative equilibrium is an attractor.

### MSC:

 39A11 Stability of difference equations (MSC2000) 39B05 General theory of functional equations and inequalities