On the approximate solution of Hosszus functional equation

Authors

1 Laboratory LIRST, Polydisciplinary Faculty, Departement of Mathematics, University Sultan Moulay Slimane, Beni-Mellal Morocco.

2 National and Capodistrian University of Athens, Section of Mathematics and Informatics, 4, Agamemnonos Str., Aghia Paraskevi, Athens 15342, Greece.

3 Faculty of sciences, Departement of Mathematics, University of Ibn Tofail, Kenitra, Morocco.

Abstract

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

Keywords