Lagrangian means

Abstract

We define Lagrangian means as those obtained from applying the classical mean value formula to a strictly convex regular function. We show that there is a close relationship between Lagrangian and quasiarithmetic means which can be made explicit through a homeomorphism. This leads to the characterization of Lagrangian means in terms of the associated quasiarithmetic ones. © Birkhäuser Verlag, Basel, 1998.