Square iterative roots of generalized weighted quasi-arithmetic mean-type mappings (Q2036562)

Let functions \(f\) and \(g\) of a single variable be of the same type monotonicity, continuous and \(f+g\) be strictly monotonic. The function of two variables \(A_{f,g}(x, y) := (f + g)^{-1} (f(x) + g(y))\) is called the bivariable strict mean. The authors solve the functional equation \((A_{f,g}, A_{g,h})\circ (A_{f,g}, A_{g,h}) = (A_{F,G}, A_{G,H})\) under three times differentiability of the functions \(f, g, h, F, G, H\).