Stability of Mixed Type Additive-Cubic Jensen Functional Equation in Non-Archimedean $(n, \beta)$ Normed Spaces

TL;DR

This paper investigates the stability of a mixed additive-cubic Jensen functional equation within non-Archimedean $(n, eta)$ normed spaces, extending the understanding of functional equation stability in these mathematical structures.

Contribution

It establishes the Hyers-Ulam stability of the mixed-type additive-cubic Jensen functional equation in non-Archimedean $(n, eta)$ normed spaces, a novel extension in this area.

Findings

Proves stability under specific non-Archimedean norms

Extends stability results to mixed additive-cubic equations

Provides conditions for stability in $(n, eta)$ spaces

Abstract

In this paper, we discuss the Hyers-Ulam stability of mixed-type additive-cubic Jensen functional equation \begin{align*} 2\mathcal{F}\left(\frac{2u+v}{2}\right)+2\mathcal{F}\left(\frac{2u-v}{2}\right)=\frac{1}{4}[\mathcal{F}(u+v)+\mathcal{F}(u-v)]+3\mathcal{F}(u) \end{align*} in non-Archimedean $(n, \beta)$ normed spaces.