Jensen's functional equation on the symmetric group ${\mathbf{S}}_{\mathbf{n}}$

Công-Trình Lê, Trung-Hiêu Thái

Two natural extensions of Jensen's functional equation on the real line are the equations $f(xy)+f(x{y}^{-1})=2f(x)$ and $f(xy)+f(y^{-1}x)=2f(x)$, where $f$ is a map from a multi…