General system of cubic–quartic functional equations in quasi-β-normed spaces

Abstract

In the current article, we define the multicubic–quartic mappings and describe them as an equation. We also study n-variable mappings, which are mixed type cubic–quartic in each variable and then give a characterization of such mappings. Indeed, we unify the general system of cubic–quartic functional equations defining a multimixed cubic–quartic mapping to a single equation, say, the multimixed cubic–quartic functional equation. Furthermore, we show under what conditions every multimixed cubic–quartic mapping can be multicubic, multiquartic and multicubic–quartic. In addition, by means of a known fixed-point result, we prove the Găvrua stability of multimixed cubic–quartic functional equations in the setting of quasi-β-normed spaces. One of the important results is that every multimixed cubic–quartic functional equation on a quasi-β-normed space is the Hyers–Ulam stable. Lastly, we investigate the hyperstability of multicubic $\ast$-derivations on $C^{\ast }$-algebras.