New equilibria of non-autonomous discrete dynamical systems

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