A one-parameter family of bivariate means (Q2855178)

It would seem unlikely that anything very new could be said about symmetric two variable means and yet here is a paper that does just that. It is well written and very lucid. Given such a mean \(N\) and a number \(p\), \(-1\leq p\leq 1,\) define \(N_p(x,y) = N\bigl({1+p\over 2}x+{1-p\over 2}y, {1-p\over 2}x+{1+p\over 2}y\bigr)\). The order relations between various standard means are well known; the same order is maintained in the new class of means when the standard means are used as \(N.\) The new class of means is studied and most if not all the important properties obtained in a very simple manner.