Any interior point of a finite interval on the real line can be interpreted as dual Fréchet means

Abstract: In this note, we show that any interior point of an open interval on the real line can be interpreted as a pair of dual Fréchet quasi-arithmetic means associated with dual metric distances. A Riemannian interpretation of the Euclidean line brings to light a novel concept of dual scales of means, grounded in convex duality and of independent interest.