The Jensen functional equation in non-Archimedean normed spaces
We investigate the Hyers–Ulam–Rassias stability of the Jensen functional equation in non-Archimedean normed spaces and study its asymptotic behavior in two directions: bounded and unbounded Jensen differences. In particular, we show that a mapping f between non-Archimedean spaces with f(0)=0 is addi...
Saved in:
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2009-01-01
|
| Series: | Journal of Function Spaces and Applications |
| Online Access: | http://dx.doi.org/10.1155/2009/802032 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Summary: | We investigate the Hyers–Ulam–Rassias stability of the Jensen
functional equation in non-Archimedean normed spaces and study its asymptotic
behavior in two directions: bounded and unbounded Jensen differences. In
particular, we show that a mapping f between non-Archimedean spaces with
f(0)=0 is additive if and only if ‖f(x+y2)−f(x)+f(y)2‖→0 as max {‖x‖,‖y‖}→∞. |
|---|---|
| ISSN: | 0972-6802 |