Characterization and stability of multi-Euler-Lagrange quadratic functional equations (Q6099064)

Summary: The aim of the current article is to characterize and to prove the stability of multi-Euler-Lagrange quadratic mappings. In other words, it reduces a system of equations defining the multi-Euler-Lagrange quadratic mappings to an equation, say, the multi-Euler-Lagrange quadratic functional equation. Moreover, some results corresponding to known stability (Hyers, Rassias, and Găvruta) outcomes regarding the multi-Euler-Lagrange quadratic functional equation are presented in quasi-\( \beta \)-normed and Banach spaces by using the fixed point methods. Lastly, an example for the nonstable multi-Euler-Lagrange quadratic functional equation is indicated.