Quartic Functional Equation: Ulam-Type Stability in β , p -Banach Space and Non-Archimedean β -Normed Space

Abstract

In this study, we use the alternative fixed-point approach and the direct method to examine the generalized Hyers–Ulam stability of the quartic functional equation $g\left(u+mv\right)+g\left(u-mv\right)=2\left(m-1\right)\left(7m-9\right)g\left(u\right)+2\left(m^2-1\right)m^{2}g\left(v\right)-{\left(m-1\right)}^{2}g\left(2u\right)+m^2\left\{g\left(u+v\right)+g\left(u-v\right)\right\},$ with a fixed positive integer $m/ge2$ in the context of $\left(\beta ,p\right)$ -Banach space. In non-Archimedean $\beta$ -normed space, we also verify Hyers–Ulam stability for the quartic functional equation stated. Many of the findings in the literature are improved and generalized by our findings.