In the framework of non-autonomous discrete dynamical systems in metric spaces, we propose new equilibrium points, called quasi-fixed points, and prove that they play a role similar to that of fixed points in autonomous discrete dynamical systems. In this way some sufficient conditions for the convergence of iterative schemes of type $x_{k+1}=T_k{x}_k$ in metric spaces are presented, where the maps $T_k$ are contractivities with different fixed points. The results include any reordering of the maps, even with repetitions, and forward and backward directions. We also prove generalizations of the Banach fixed point theorems when the self-map is substituted by a sequence of contractivities with different fixed points. The theory presented links the field of dynamical systems with the theory of iterated function systems. We prove that in some cases the set of quasi-fixed points is an invariant fractal set. The hypotheses relax the usual conditions on the underlying space for the existence of invariant sets in countable iterated function systems.

在度量空间中的非自治离散动力系统框架中，我们提出了新的平衡点，称为拟不动点，并证明它们的作用类似于自治离散动力系统中不动点的作用。以这种方式使类型的迭代方案收敛的一些充分条件$X_{克+1}={吨}_{克}{X}_{克}$ 在度量空间中呈现，其中映射 ${吨}_{克}$是具有不同不动点的收缩性。结果包括对地图的任何重新排序，即使有重复，以及向前和向后方向。我们还证明了当自映射被具有不同不动点的一系列收缩性取代时巴拿赫不动点定理的推广。提出的理论将动力系统领域与迭代函数系统理论联系起来。我们证明在某些情况下，准不动点集是一个不变的分形集。这些假设放宽了可数迭代函数系统中存在不变集的潜在空间的通常条件。