On an equation involving weighted quasi-arithmetic means.

Let I ⊂ ℝ be an interval and κ, λ ∈ ℝ / {0, 1}, µ, ν ∈ (0, 1). We find all pairs ( φ, ψ) of continuous and strictly monotonic functions mapping I into ℝ and satisfying the functional equation which generalizes the Matkowski-Sutô equation. The paper completes a research stemming in the theory of invariant means. [ABSTRACT FROM AUTHOR]