On a pexiderized conditional exponential functional equation

We study the exponential functional equation f(x+y) = f(x)f(y) for (x; y) ∈ D ? X × X, where X is the domain of f. Regardless of the solutions of this equation, which in many special cases are already known, we investigate its stability and consider its pexiderized version. The intention of the paper is to give quite general approach to the studies of this subject as well as to describe the properties of D so that the results include those concerning orthogonal and some other conditional exponential equations.