Asymptotic Stability of the Pexider-Cauchy Functional Equation in Non-Archimedean Spaces

In this paper, we investigated the asymptotic stability behaviour of the Pexider-Cauchy functional equation in non-Archimedean spaces. We also showed that, under some conditions, if parallel to f (x + y) - g(x) - h(y)parallel to <= epsilon, then f, g and h can be approximated by additive mapping in non-Archimedean normed spaces. Finally, we deal with a functional inequality and its asymptotic behaviour.

Automated summary

This paper investigates the asymptotic stability behavior of the Pexider-Cauchy functional equation in non-Archimedean spaces, and shows that under certain conditions, f, g, and h can be approximated by additive mapping in non-Archimedean normed spaces. Additionally, it deals with a functional inequality and its asymptotic behavior.