We consider the perturbed Mann’s iterative process \begin{equation}
x_{n+1}=(1-\theta_n)x_n+\theta_n f(x_n)+r_n, \end{equation} where
$f:[0,1]\rightarrow[0,1]$ is a continuous function, $\{\theta_n\}\in [0,1]$ is
a given sequence, and $\{r_n\}$ is the error term. We establish that if the
sequence $\{\theta_n\}$ converges relatively slowly to $0$ and the error term
$r_n$ becomes enough small at infinity, any sequences $\{x_n\}\in [0,1]$
satisfying the process converges to a fixed point of the function $f$. We also
study the asymptotic behavior of the trajectories $x(t)$ as
$t\rightarrow\infty$ of a continuous version of the the considered. We
investigate the similarities between the asymptotic behaviours of the sequences
generated by the considered discrete process and the trajectories $x(t)$ of its
corresponding continuous version.

Este artículo explora los viajes en el tiempo y sus implicaciones.

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