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

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
$$|f(x+y+xy)-f(x)-f(y)-f(xy)|\le \delta +\phi (x;y)$$
for any $x,y\in \mathbb{R}$ and $\delta >0$.

Keywords

• Additive function
• Hosszu's functional equation
• Hyers-Ulam stability