In this paper, we modify the Cauchy additive functional equation and find all solutions of this new functional equation. Then, we study generalized Ulam-Hyers stability of such functional equation in various Banach spaces via Hyers' method.
"Approximate $n$-dimensional additive functional equation in various Banach spaces." Tbilisi Math. J. 11 (2) 77 - 96, June 2018. https://doi.org/10.32513/tbilisi/1529460024