Fibonacci mean and golden section mean

In this paper we show that there is a mapping D:M→DMD:M→DM on means such that if MM is a Fibonacci mean so is DMDM, that if MM is the harmonic mean, then DMDM is the arithmetic mean, and if MM is a Fibonacci mean, then limn→∞DnMlimn→∞DnM is the golden section mean.