Stability of a general functional equation in \(m\)-Banach spaces (Q2683163)

The author studies the Ulam stability of a general functional equation in several variables. More specifically, it is shown that a generalization of the Jordan-von Neumann functional equation is Ulam stable in \(m\)-Banach spaces, i.e., \(m\)-normed spaces such that each Cauchy sequence is convergent. Additionally, the stability of a functional equation considered in [\textit{P. Ji} et al., J. Math. Res. Appl. 34, No. 2, 209--215 (2014; Zbl 1313.39039); \textit{X. Zhao} et al., Abstr. Appl. Anal. 2013, Article ID 415053, 8 p. (2013; Zbl 1291.39057)] for the characterization of multiquadratic mappings is investigated.