A general system of quadratic functional equations in non-Archimedean fuzzy Menger normed spaces (Q2917780)

The concept of stability for a functional equation arises when one replaces the functional equation by an inequality, which acts as a perturbation of the equation. In the 1940, S. M. Ulam posed the first stability problem. In the following year, \textit{D. H. Hyers} [Proc. nat. Acad. Sci. USA 27, 222--224 (1941; JFM 67.0424.01)] gave a partial affirmative answer to the question of Ulam. Hyers' theorem was generalized by \textit{T. Aoki} [J. Math. Soc. Japan 2, 64--66 (1950; Zbl 0040.35501)] for additive mappings and by \textit{Th. M. Rassias} [Proc. Am. Math. Soc. 72, 297--300 (1978; Zbl 0398.47040)] for linear mappings by considering an unbounded Cauchy difference. In the present work, the authors prove the generalized Hyers-Ulam-Rassias stability for a general system of quadratic functional equations in non-Archimedean fuzzy Menger normed spaces.