KONG Liang, CAO Huai-xin
(College of Mathematics and information Science, Shaanxi Normal University, Xi′an 710062, Shaanxi, China)
Abstract:
To study stability of orthogonality preserving mappings, the (δ，ε)-approximately orthogonality preserving mapping is introduced, which is proved to be bounded. It is proved that linear orthogonality preserving mapping is stable in the sense of linear (δ，ε)-approximately orthogonality preserving. A sufficient condition for a linear mapping to be a (δ，ε)-approximately orthogonality preserving mapping is given. Stability of the orthogonality equation is established.
KeyWords:
stability; orthogonality preserving mapping; orthogonality equation; ε-approximately orthogonality preserving mapping; (δ，ε)-approximately orthogonality preserving mapping
