Approximation on a system of equations driving from mixed type additive and quartic functional equations

Abstract

In the current investigation, we introduce a novel multimixed additive-quartic mapping as a system of mixed additive and quartic functional equations. Then we represent and characterize this system of functional equations as a single equation. We find some relations between this new definition and multi-additive and multi-quartic mappings by using linear and quartic conditions. Moreover, we show that each multimixed additive-quartic mapping can be reduced into either multi-additive or multi-quartic mapping. Furthermore, we prove the Hyers–Ulam stability of multimixed additive-quartic functional equations in the content of quasi-𝛽-2-Banach spaces. Eventually, we provide some known stability outcomes when the controller bound changes.