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A distributed algorithm is described for finding a common fixed point of afamily of $m>1$ nonlinear maps $M_i : \mathbb{R}^n \rightarrow \mathbb{R}^n$assuming that each map is a paracontraction and that such a common fixed pointexists. The common fixed point is simultaneously computed by $m$ agentsassuming each agent $i$ knows only $M_i$, the current estimates of the fixedpoint generated by its neighbors, and nothing more. Each agent recursivelyupdates its estimate of the fixed point by utilizing the current estimatesgenerated by each of its neighbors. Neighbor relations are characterized by atime-dependent directed graph $\mathbb{N}(t)$ whose vertices correspond toagents and whose arcs depict neighbor relations. It is shown that for anyfamily of paracontractions $M_i, i \in \{1,2,\ldots,m\}$ which has at least onecommon fixed point, and any sequence of strongly connected neighbor graphs$\mathbb{N}(t)$, $t=1,2,\ldots$, the algorithm causes all agent estimates toconverge to a common fixed point.

A Distributed Algorithm for Computing a Common Fixed Point of a Family of Paracontractions