Stability Results for Some Functional Equations on 2-Banach Spaces With Restricted Domains

M. R. Abdollahpour, A. Najati and Y. Khedmati Yengejeh

Journal of Mathematics, 2025, vol. 2025, 1-9

Abstract: 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.

Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jjmath:8405645

DOI: 10.1155/jom/8405645

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