On means generated through the Cauchy mean value theorem

Cauchy means are defined as those obtained from applying the Cauchy mean value theorem to a pair of suitable functions. A so-called mixing operator is defined, in such a way that each Cauchy mean is the unique fixed point of the mixing operator associated with two quasiarithmetic means. As a consequence, some comparison results for Cauchy means are obtained, together with a functional characterization relating a subclass of Cauchy means, the so-called anti-Lagrangian means, with quasiarithmetic ones.