Stability Results for Some Functional Equations on 2-Banach Spaces With Restricted Domains - M. R. Abdollahpour; A. Najati; Y. Khedmati Yengejeh (Journal of Mathematics)
We have a normed abelian group G,.∗,+ and a 2-pre-Hilbert space Y with linearly independent elements u and v. Our goal is to prove that any odd map f:G⟶Y satisfying the inequality fx+fy,z⩽fx+y,z,z∈u,v, for all x,y∈G with x∗+y∗≥d and some d≥0, is additive. Then, we examined the stability issue correlated with Cauchy and Jensen functional inequalities on restricted domains for maps from normed abelian groups to 2-Banach spaces. In addition, we determined the asymptotic behaviors of these functional equations.