The way of all means

We are interested in presenting some problems concerning the limits of mean iterations. For our current purposes, a mean is a continuous real-valued function M of two strictly positive real variables a and b so that, for all such a and b min(a,b) ≤ M(a,b) ≤ max(a,b). This inequality, which ensures that M(a,b) lies bewtween a and b, is the absolutely essential part of the definition.