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

Articles in Press

Document Type : Original Article

Authors

Department of Mathematics, West Tehran Branch, Islamic Azad University, Tehran, Iran

Abstract

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.

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AUT Journal of Mathematics and Computing

Articles in Press, Accepted Manuscript
Available Online from 03 July 2025

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