  We show that the moving arithmetic average is closely connected to a
Gauss-Seidel type fixed point method studied by Bauschke, Wang and Wylie, and
which was observed to converge only numerically. Our analysis establishes a
rigorous proof of convergence of their algorithm in a special case; moreover,
limit is explicitly identified. Moving averages in Banach spaces and Kolmogorov
means are also studied. Furthermore, we consider moving proximal averages and
epi-averages of convex functions.
