Integral functional equations on locally compact groups with involution (Q329390)

The main theorem of the paper gives the solutions of the following functional equation: \[ f(x\sigma(y))+f(\tau(y)x)=2f(x)g(y),\qquad x,y\in M, \] where \(M\) is a group or a monoid, \(\sigma,\tau: M\to M\) are involutive automorphisms, and \(f,g: M\to\mathbb{C}\) are the unknown functions.