Stability of cubic and quartic functional equations in non-Archimedean spaces

TL;DR

This paper establishes the stability of specific cubic and quartic functional equations within non-Archimedean spaces, extending the understanding of their behavior under perturbations in such mathematical frameworks.

Contribution

It proves generalized Hyers-Ulam-Rassias stability for cubic and quartic functional equations in non-Archimedean normed spaces, a novel extension in this area.

Findings

Stability results for cubic functional equations in non-Archimedean spaces.

Stability results for quartic functional equations in non-Archimedean spaces.

Extension of Hyers-Ulam-Rassias stability to these equations.

Abstract

We prove generalized Hyres-Ulam-Rassias stability of the cubic functional equation $f(kx+y)+f(kx-y)=k[f(x+y)+f(x-y)]+2(k^3-k)f(x)$ for all $k\in \Bbb N$ and the quartic functional equation $f(kx+y)+f(kx-y)=k^2[f(x+y)+f(x-y)]+2k^2(k^2-1)f(x)-2(k^2-1)f(y)$ for all $k\in \Bbb N$ in non-Archimedean normed spaces.