On the approximate solution of Hosszus functional equation

نویسندگان
Charifi, A. ID 1
Bouikhalene, B. ID 2
Rassias, J. M. ID 3
Kabbaj, S. ID 4

1 Faculty of sciences, Departement of Mathematics, University of Ibn Tofail, Kenitra, Morocco

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

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

4 Faculty of sciences, Departement of Mathematics, University of Ibn Tofail, Kenitra, Morocco

doi
10.22075/ijnaa.2012.45
چکیده

We show that every approximate solution of the Hosszu's functional equation$$f(x + y + xy) = f(x) + f(y) + f(xy) \ \text{for any}\ x, y\in \mathbb{R},$$is an additive function and also we investigate the Hyers-Ulam stability of this equation in the following setting$$|f(x + y + xy) - f(x) - f(y) - f(xy)|\leq\delta + \varphi(x; y)$$for any $x, y\in \mathbb{R}$ and $\delta > 0$.

کلیدواژه‌ها
Additive function, Hosszu's functional equation, Hyers-Ulam stability