Pexider Equation on a Restricted Domain

On functional equation stemming from utility theory and psychophysics

“…Since σ is continuous and σ |(y0,y0+z0) is nonconstant, the latter set is a nonempty open and connected subset of (0, ∞) 2 . Therefore, as f (y0) is nonconstant, according to [5,Corollary 2], there exist a multiplicative function m : (0, ∞) → R \ {0} and a ∈ R \ {0} such that f (y0) (z) = am(z) for z ∈ (z 0 , ∞). Hence, in view of (16), we get…”