| Popis: |
Suppose that $\mathcal{X}$ is a sequentially complete Hausdorff locally convex space over a scalar field $\mathbb{K}$, $V$ is a bounded subset of $\mathcal{X}$, $(a_n)_{n\ge 0}$ is a sequence in $\mathbb{K}\setminus\{0\}$ with the property\ $\ds\liminf_{n\to\infty} |a_n|>1$ and $(b_n)_{n\ge 0}$ is a sequence in $\mathcal{X}$. We show that for every sequence $(x_n)_{n\ge 0}$ in $\mathcal{X}$ satisfying \begin{eqnarray*} x_{n+1}-a_nx_n-b_n\in V\q(n\geq 0) \end{eqnarray*} there exists a unique sequence $(y_n)_{n\ge 0}$ satisfying the recurrence $y_{n+1}=a_ny_n+b_n\,\,(n\geq 0)$ and for every $q$ with $1Comment: 13 pages, to appear in Nonlinear Analysis: Theory, Methods & Applications |
