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

Abstract

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 ∥f(x+y)−g(x)−h(y)∥⩽ε, 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.

Keywords

• non-Archimedean space
• Pexider–Cauchy equation
• asymptotic stability