Equivalence for various forms of quadratic functional equations and their generalized Hyers-Ulam-Rassias stability (Q6156265)

Summary: In this manuscript, we study the properties and equivalence results for different forms of quadratic functional equations. Using the Brzdȩk and Ciepliński fixed-point approach, we investigate the generalized Hyers-Ulam-Rassias stability for the 3-variables quadratic functional equation in the setting of 2-Banach space. Also, we obtain some hyperstability results for the 3-variables quadratic functional equation. The results obtained in this paper extend several known results of the literature to the setting of 2-Banach space.