Characterization and stability analysis of the advanced multi-quadratic functional equations

In this paper, we introduce a new quadratic functional equation and by using this equation, we investigate $n$-variables mappings which are quadratic in each variable. We show that such mappings can be unified as an equation, namely, multi-quadratic functional equation. We also apply a fixed point technique to study the stability for the multi-quadratic functional equations. Furthermore, we present an example and a few corollaries corresponding to some known stability and hyperstability outcomes.