On a class of means of two variables
Zoltán Daróczy · Publicationes Mathematicae Debrecen · 1999
Let CM (I) denote the class of all continuous and strictly monotonic real functions defined on the interval I. Let L : I 2 → I be a fixed mean on I.A mean M : I 2 → I is called an L-conjugate mean on I if there exists ϕ ∈ CM (I) for which M (x, y) = L * ϕ (x, y) := ϕ -1 (ϕ(x) + ϕ(y) -ϕ(L(x, y))) holds for all x, y ∈ I.We solve the following problems for L-conjugate means: equality, comparison, determining homogeneous and translative means and inequalities involving them.Furthermore, we examine when such a mean is quasi-arithmetic, if L = A, where A is the arithmetic mean.