Note on a functional equation related to the power means
Solutions of the functional equation \( x + g(y + f(x)) = y + g(x + f(y)) \) are determined under the assumption that (at least) one of the unknown functions is additive or has the form of a weighted quasi-arithmetic mean with an exponential generator. Continuity assumptions are required when \(f\) is supposed to belong to a given class.
scientific article; zbMATH DE number 1604180