\(M\)-affine functions composing Sturm-Liouville families
The authors prove results related to the functional equation \[ f(M(x_1,\dots, x_n))= M(f(x_1),\dots, f(x_n)), \] where \(M\) is an \(n\)-variable mean. Particularly, when \(M\) is a quasilinear mean, connections with the so-called Sturm-Liouville family of functions are considered. As applications, new characterizations of quasilinear means are provided.
scientific article; zbMATH DE number 6944064