On the approximate solution of Hosszus functional equation

Abstract

We show that every approximate solution of the Hossz u's functional<br />equation<br />f(x + y + xy) = f(x) + f(y) + f(xy) for any x; y 2 R;<br />is an additive function and also we investigate the Hyers-Ulam stability of this<br />equation in the following setting<br />jf(x + y + xy) 􀀀 f(x) 􀀀 f(y) 􀀀 f(xy)j + '(x; y)<br />for any x; y 2 R and > 0.