Stability of generalized mixed type additive-quadratic-cubic functional equation in non-Archimedean spaces

TL;DR

This paper investigates the stability of a complex functional equation involving additive, quadratic, and cubic components within non-Archimedean spaces, extending the understanding of such equations' robustness under perturbations.

Contribution

It establishes the generalized Hyers-Ulam-Rassias stability for a mixed type functional equation in non-Archimedean spaces, a novel extension in this mathematical context.

Findings

Proves stability of the functional equation in non-Archimedean spaces.

Extends stability results to mixed additive-quadratic-cubic equations.

Provides conditions under which the stability holds.

Abstract

In this paper, we prove generalized Hyres--Ulam--Rassias stability of the mixed type additive, quadratic and cubic functional equation $$f(x+ky)+f(x-ky)=k^2f(x+y)+k^2f(x-y)+2(1-k^2)f(x)$$ for fixed integers $k$ with $k\neq0,\pm1$ in non-Archimedean spaces.