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In 1940, Ulam 1 gave a talk before the Mathematics Club of the University of Wisconsin in which he discussed a number of unsolved problems, containing the stability problem of homomorphisms as follows 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… (More)

In 1940, Ulam proposed the general Ulam 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… (More)

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… (More)

and Applied Analysis 3 Theorem 2.2. A mapping f : X ×X → Y satisfies 1.1 if and only if it satisfies 1.2 . Proof. If f satisfies 1.1 , then we get

In this paper, we determine some stability results concerning the 2-dimensional vector variable quadratic functional equation f(x+ y, z + w) + f(x − y, z − w) = 2f(x, z) + 2f(y, w) in intuitionistic fuzzy normed spaces (IFNS). We define the intuitionistic fuzzy continuity of the 2-dimensional vector variable quadratic mappings and prove that the existence… (More)

- Jae-Hyeong Bae, Won-Gil Park
- Applied Mathematics and Computation
- 2010

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… (More)

- Jae-Hyeong Bae
- 2003

We prove the generalized Hyers-Ulam-Rassias stability of a partitioned functional equation. It is applied to show the stability of algebra homomorphisms between Banach algebras associated with partitioned functional equations in Banach algebras.