On homogeneous Lagrange means (Q397081)

This work focuses on the properties of Lagrangian means. After an introduction, some known things are collected. The third section is about the equality of Lagrangian means. The main result of this part characterizes the relationship between the generators when the derivative is one-to-one. The main theorem of the fourth section states that positive homogeneity of a Lagrangian mean implies infinitely many time differentiability of the generator. In the fifth section, conditionally homogeneous Lagrangian means are characterized, and in the last one, there are corollaries about Cauchy means which are close relatives of Lagrangian means.