“Pexiderized” homogeneity almost everywhere

Abstract: In the paper we examine Pexiderized ϕ-homogeneity equation almost everywhere. Assume that G and H are groups with zero, and are a G- and an H-space, respectively. We prove, under some assumption on , that if functions and satisfy Pexiderized ϕ-homogeneity equation almost everywhere in then either almost everywhere in G or almost everywhere in X or there exists a homomorphism such that almost everywhere in G and there exists a function such that and where is a constant. From this result we derive solution of the classical Pexider equation almost everywhere. [Copyright &y& Elsevier]