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(_i=1^nx_i)=_i=1^nf(x_i) in Banach spaces. Namely, we show that a function satisfying the equation approximately must be actually a solution to it.