The Fréchet Functional Equation for Lie Groups ; Belgique

peer reviewed ; We study a generalization of the Fréchet functional equation in the setting of Lie groups. We provide theorems that give a description of the solutions and their regularity. These properties are applied to obtain new results about the Fréchet functional equations generalized to homogeneous spaces. In the end, we present a few examples and counterexamples. ; Generalizations of difference operator and Cauchy functional equations