Generalized Hyers–Ulam stability of mixed-type additive-quartic mappings in 2-Banach spaces

Abstract This paper aims to explore the stability of a mixed-type additive-quartic functional equation in 2-Banach spaces via the direct method. We categorize mappings satisfying a certain functional inequality into odd, even, and general mappings, and establish generalized Hyers–Ulam stability for each category. For odd mappings, we demonstrate that the exact solution, represented by an additive mapping, is close to the approximate solution satisfying the functional inequality. For even mappings, the exact solution, represented by a quartic mapping, is close to the approximate solution. Furthermore, we show that for general mappings, the exact solution, represented by the sum of an additive and a quartic mapping, is close to the approximate solution.