@article {
author = {Bouikhalene, B. and Rassias, J. M. and Charifi, A. and Kabbaj, S.},
title = {On the approximate solution of Hosszus functional equation},
journal = {International Journal of Nonlinear Analysis and Applications},
volume = {3},
number = {1},
pages = {40-44},
year = {2012},
publisher = {Semnan University},
issn = {2008-6822},
eissn = {2008-6822},
doi = {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},
url = {https://ijnaa.semnan.ac.ir/article_45.html},
eprint = {https://ijnaa.semnan.ac.ir/article_45_05a87c012c6971554afb7ebdaa886d7d.pdf}
}