Stability of a Bi-Additive Functional Equation in Banach Modules Over a C -Algebra
نویسندگان
چکیده
In 1940, Ulam proposed the stability problem see 1 . Let G1 be a group, and let G2 be a metric group with the metric d ·, · . Given ε > 0, does there exist a δ > 0 such that if a mapping h : G1 → G2 satisfies the inequality d h xy , h x h y < δ for all x, y ∈ G1 then there is a homomorphism H : G1 → G2 with d h x ,H x < ε for all x ∈ G1? In 1941, this problem was solved by Hyers 2 in the case of Banach space. Thereafter, many authors investigated solutions or stability of various functional equations see 3–21 . Let X and Y be real or complex vector spaces. In 1989, Aczél and Dhombres 22 proved that a mapping g : X → Y satisfies the quadratic functional equation
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