ABSTRACT
In this chapter, we prove the stability of the Hosszu´ functional equation and a functional equation that generalizes the Hosszu´ functional equation. In 1993, Kannappan and Sahoo determined the general solution f, g, h, k : R→ R of the functional equation
f(x+ y − αxy) + g(xy) = h(x) + k(y) (23.1) for all x, y ∈ R (see also Ebanks, Kannappan and Sahoo (1992b)). Here α is an a priori chosen parameter. If α = 1, then (23.1) is a pexiderized version of the Hosszu´ functional equation, namely,
f(x+ y − xy) + f(xy) = f(x) + f(y). If α = 0, then (23.1) reduces to
f(x+ y) + g(xy) = h(x) + k(y).
