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 $\delta > 0$.
Bouikhalene, B., Rassias, J. M., Charifi, A. & Kabbaj, S. (2012). On the approximate solution of Hosszus functional equation. International Journal of Nonlinear Analysis and Applications, 3(1), 40–44. https://doi.org/10.22075/ijnaa.2012.45
MLA
Bouikhalene, B., Rassias, J. M., Charifi, A., & Kabbaj, S. "On the approximate solution of Hosszus functional equation", International Journal of Nonlinear Analysis and Applications, 3, 1, 2012, 40–44. doi: 10.22075/ijnaa.2012.45
HARVARD
Bouikhalene, B., Rassias, J. M., Charifi, A., & Kabbaj, S. (2012). 'On the approximate solution of Hosszus functional equation', International Journal of Nonlinear Analysis and Applications, 3(1), pp. 40–44. doi: 10.22075/ijnaa.2012.45
CHICAGO
Bouikhalene, B., Rassias, J. M., Charifi, A. & Kabbaj, S., "On the approximate solution of Hosszus functional equation." International Journal of Nonlinear Analysis and Applications, 3 1 (2012): 40–44, doi: 10.22075/ijnaa.2012.45
VANCOUVER
Bouikhalene B., Rassias J. M., Charifi A., Kabbaj S. On the approximate solution of Hosszus functional equation. IJNAA. 2012;3(1):40–44. doi: 10.22075/ijnaa.2012.45
International Journal of Nonlinear Analysis and Applications