HYPERSTABILITY OF A CAUCHY FUNCTIONAL EQUATION - Almahalebi, M.; Charifi, A.; Kabbaj, S. (Journal of Nonlinear Analysis and Optimization: Theory & Applications (JNAO), 2016)
The aim of this paper is to offer hyperstability results for the Cauchy functional equation $$f\left(\sum_{i=1}^{n}x_{i}\right)=\sum_{i=1}^{n}f(x_{i})$$ in Banach spaces. Namely, we show that a function satisfying the equation approximately must be actually a solution to it.