| |
|
|
| |
Volume 7, Issue 3, Article 85 |
|
|
|
|
|
| |
On Some Approximate Functional Relations Stemming from Orthogonality Preserving Property
|
| |
|
Authors: |
Jacek Chmielinski, |
|
| |
|
Keywords:
|
Orthogonality preserving mappings, Right-angle preserving mappings, Preservation of the inner product, Stability of functional equations. |
|
| |
|
Date Received:
|
17/01/06 |
|
| |
|
Date Accepted:
|
24/02/06 |
|
| |
|
Subject Codes: |
39B52, 39B82, 47H14.
|
|
| |
|
Editors: |
Kazimierz Nikodem, |
|
| |
|
|
|
|
|
| |
|
Abstract: |
Referring to previous papers on orthogonality preserving mappings we deal with some relations, connected with orthogonality, which are preserved exactly or approximately. In particular, we investigate the class of mappings approximately preserving the right-angle. We show some properties similar to those characterizing mappings which exactly preserve the right-angle. Besides, some kind of stability of the considered property is established. We study also the property that a particular value  of the inner product is preserved. We compare the case  with  , i.e., with orthogonality preserving property. Also here some stability results are given.
|
|
|
|
|
|
| |
|
|
|
|
| |
|
|
|
|
|
Home
