Amirkabir University of Technology AUT Journal of Mathematics and Computing 2783-2449 7 4 2026 10 01 Characterization and the stability of a system of multi-radical mappings related to the additive mapping 467 477 5787 10.22060/ajmc.2025.23946.1341 EN Abasalt Bodaghi Department of Mathematics, West Tehran Branch, Islamic Azad University, Tehran, Iran Sedigheh Hosseini Department of Mathematics, Kermanshah Branch, Islamic Azad University, Kermanshah, Iran Journal Article 2025 02 24 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 $\mathbb R^m$, we investigate the stability of a mapping $f:\mathbb R^{mn}\longrightarrow \mathbb R^{m}$ by a known fixed point method. https://ajmc.aut.ac.ir/article_5787_a32d7eeaae19821fd9ce317f3ce952a7.pdf