On the approximate solution of Hosszus functional equation

Bouikhalene, B.; Rassias, J. M.; Charifi, A.; Kabbaj, S.

doi:10.22075/ijnaa.2012.45

On the approximate solution of Hosszus functional equation

Document Type : Research Paper

Authors

B. Bouikhalene ¹

J. M. Rassias ²

A. Charifi ³

S. Kabbaj ³

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

10.22075/ijnaa.2012.45

Abstract

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 $\delta > 0$.

Keywords

Additive function

Hosszu's functional equation

Hyers-Ulam stability