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Stability of an AQCQ functional equation in non-Archimedean (n, β)-normed spaces

Liu Yachai, Yang Xiuzhong, Liu Guofen

Demonstratio Mathematica

2019

Vol. 52, nr 1

130--146

In this paper, we adopt direct method to prove the Hyers-Ulam-Rassias stability of an additive-quadratic-cubic-quartic functional equation f(x+2y)+f(x-2y) = 4f(x+y)+4f(x-y)-6f(x)+f(2y)+f(-2y)-4f(y)-4f(-y) in non-Archimedean (n,β)-normed spaces.

Note on the stability of the system of functional equations

Adam M.

Silesian Journal of Pure and Applied Mathematics

2017

Vol. 7, iss. 1

93--98

We deal with the system of functional equations connected with additive and quadratic mappings. We correct some mistakes made in the paper [W. Fechner, On the Hyers-Ulam stability of functional equations connected with additive and quadratic mappings, J. Math. Anal. Appl. 322 (2006), 774–786] and provide accurate statements of those results. Moreover, we get the improvement of the Hyers-Ulam stability result of the considered system of functional equations.