On perturbations of the multiadditive mappings via the concept of generalized <i>Z</i> -numbers

It is known that the best decision directly depends on the most exact approximation. To obtain the best quality and certainty of a proximity to the exact solution of a multiadditive mapping, we aim to quantify both the certainty and quality of the approximation and errors as well. In the current investigation, we define a generalized form of multiadditive mappings (different from existing formulations). Then, we represent such mappings (defined as a novel comprehensive system of additive functional equations) as one unified single equation. In some cases, we show that an equation can describe a multiadditive mapping and vice versa (under some mild conditions). In continuation, by applying a fixed point manner, we give a control function to study Găvruţa and Rassias stability to approximate the solution of the mentioned equation with quality and certainty of the approximation by applying the concept of generalized Z-numbers. Furthermore, we demonstrate some examples and applications of Hyers and Rassias stability. As a few outcomes, we give a concrete and explicit example for 2-dimensional mappings on R2 as well as on Banach algebras. Lastly, an application of Hyers stability in decision theory is given.