APPROXIMATE QUADRATIC MAPPINGS IN QUASI-β-NORMED SPACES

Approximate Quartic and Quadratic Mappings in Quasi-Banach Spaces

The stability problem of functional equations originated from a question of Ulam 1 in 1940, concerning the stability of group homomorphisms. Let G1, · be a group, and let G2, ∗ be a metric group with the metric d ·, · . Given > 0, does there exist a δ > 0 such that if a mapping h : G1 → G2 satisfies the inequality d h x · y , h x ∗ h y < δ for all x, y ∈ G1, then there exists a homomorphism H :...

Stability Problems of Quintic Mappings in Quasi--Normed Spaces

Approximate additive and quadratic mappings in 2-Banach spaces and related topics

Won{Gil Park [Won{Gil Park, J. Math. Anal. Appl., 376 (1) (2011) 193{202] proved the Hyers{Ulam stability of the Cauchy functional equation, the Jensen functional equation and the quadraticfunctional equation in 2{Banach spaces. One can easily see that all results of this paper are incorrect.Hence the control functions in all theorems of this paper are not correct. In this paper, we correctthes...

On the Stability of Cubic Mappings and Quadratic Mappings in Random Normed Spaces

1 Youngs Researchers Club and Department of Basic Sciences, Islamic Azad University, Ayatollah Amoli Branch, P.O. Box 678, Amol, Iran 2 Department of Mathematics Education and the RINS, Gyeongsang National University, Chinju 660-701, South Korea 3 Department of Mechanical Engineering, Islamic Azad University, Ayatollah Amoli Branch, P.O. Box 678, Amol, Iran 4 Department of Mathematics and Compu...

Approximate Behavior of Bi-Quadratic Mappings in Quasinormed Spaces

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 inequality d h xy , h x h y < δ for a...