Comparative Results on Stability Analysis for Three Dimensional Functional Equations

This study investigates the stability of a three-dimensional cubic functional equation within several mathematical frameworks, including $(n, \beta)$-normed spaces, non-Archimedean $(n, \beta)$-normed spaces, and random normed spaces. The theoretical stability results are validated through experimental approaches, offering practical insight into the behavior of these functional equations. A comparative analysis is provided, highlighting differences in stability dynamics across the various spaces. Notably, the introduction of $(n, \beta)$-normed spaces and their non-Archimedean counterparts presents a novel framework for analyzing stability, while the inclusion of random normed spaces adds a stochastic dimension to the analysis. The experimental validation further strengthens the practical application of the stability results, distinguishing this study from traditional approaches.