Characterization and the stability of a system of multi-radical mappings related to the additive mapping

In the current investigation, we define s-multi-radical mappings, characterize the structure of such mappings and then obtain an equation for describing them. In fact, we find a necessary and sufficient condition for a multiple mapping to be s-multi-radical. We also deal with the Hyers-Ulam stability in the spirit of Gavruta for an s-multi-radical equation by applying the so-called direct (Hyers) method in the setting of 2-Banach spaces. For a typical case, by means of a norm, induced from a 2-norm of Rᵐ, we investigate the stability of a mapping f: Rᵐⁿ Rᵐ by a known fixed point method.