On Asymptotic Behavior of a 2-Linear Functional Equation

In this paper, we deal with a 2-linear functional equation. The Hyers-Ulam stability of this functional equation is shown on some restricted unbounded domains, and the obtained results are applied to get several hyperstability consequences. Moreover, some asymptotic behaviors of 2-linear functions are investigated. We also study the Hyers-Ulam stability and superstability of the 2-linear functional equation in 2-Banach spaces.

Automated summary

In this paper, we investigate the stability and superstability of a class of 2-linear functional equations. The Hyers-Ulam stability is proven on restricted unbounded domains, and the obtained results are used to derive several hyperstability consequences. Furthermore, we study the asymptotic behaviors of 2-linear functions and the Hyers-Ulam stability and superstability of the 2-linear functional equation in 2-Banach spaces.