On the Hyers-Ulam Stability of ψ-Additive Mappings Original Research Article

Let E1 be a real normed vector space and E2 a real Banach space. S. M. Ulam posed the problem: When does a linear mapping near an approximately additive mapping ƒ: E1 → E2 exist? We give a new generalized solution to Ulam′s problem for ψ-additive mappings. Some relations with the asymptotic differentiability are also indicated.