On the Stability of Cubic Mappings and Quadratic Mappings in Random Normed Spaces
Recently, the stability of the cubic functional equation f(2x+y)+f(2x−y)=2f(x+y)+2f(x−y)+12f(x) in fuzzy normed spaces was proved in earlier work; and the stability of the additive functional equations f(x+y)=f(x)+f(y), 2f((x+y)/2)=f(x)+f(y) in random normed spaces was proved a...
| Format: | Article |
|---|---|
| Language: | English |
| Published: |
SpringerOpen
2009-02-01
|
| Series: | Journal of Inequalities and Applications |
| Online Access: | http://dx.doi.org/10.1155/2008/902187 |
| id |
doaj-a572b211db3b4465addaca74b33d469c |
|---|---|
| record_format |
Article |
| spelling |
doaj-a572b211db3b4465addaca74b33d469c2020-11-24T20:51:43ZengSpringerOpenJournal of Inequalities and Applications1025-58341029-242X2009-02-01200810.1155/2008/902187On the Stability of Cubic Mappings and Quadratic Mappings in Random Normed SpacesRecently, the stability of the cubic functional equation f(2x+y)+f(2x−y)=2f(x+y)+2f(x−y)+12f(x) in fuzzy normed spaces was proved in earlier work; and the stability of the additive functional equations f(x+y)=f(x)+f(y), 2f((x+y)/2)=f(x)+f(y) in random normed spaces was proved as well. In this paper, we prove the stability of the cubic functional equation f(2x+y)+f(2x−y)=2f(x+y)+2f(x−y)+12f(x) in random normed spaces by an alternative proof which provides a better estimation. Finally, we prove the stability of the quartic functional equation f(2x+y)+f(2x−y)=4f(x+y)+4f(x−y)+24f(x)−6f(y) in random normed spaces. http://dx.doi.org/10.1155/2008/902187 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| title |
On the Stability of Cubic Mappings and Quadratic Mappings in Random Normed Spaces |
| spellingShingle |
On the Stability of Cubic Mappings and Quadratic Mappings in Random Normed Spaces Journal of Inequalities and Applications |
| title_short |
On the Stability of Cubic Mappings and Quadratic Mappings in Random Normed Spaces |
| title_full |
On the Stability of Cubic Mappings and Quadratic Mappings in Random Normed Spaces |
| title_fullStr |
On the Stability of Cubic Mappings and Quadratic Mappings in Random Normed Spaces |
| title_full_unstemmed |
On the Stability of Cubic Mappings and Quadratic Mappings in Random Normed Spaces |
| title_sort |
on the stability of cubic mappings and quadratic mappings in random normed spaces |
| publisher |
SpringerOpen |
| series |
Journal of Inequalities and Applications |
| issn |
1025-5834 1029-242X |
| publishDate |
2009-02-01 |
| description |
Recently, the stability of the cubic functional equation f(2x+y)+f(2x−y)=2f(x+y)+2f(x−y)+12f(x) in fuzzy normed spaces was proved in earlier work; and the stability of the additive functional equations f(x+y)=f(x)+f(y), 2f((x+y)/2)=f(x)+f(y) in random normed spaces was proved as well. In this paper, we prove the stability of the cubic functional equation f(2x+y)+f(2x−y)=2f(x+y)+2f(x−y)+12f(x) in random normed spaces by an alternative proof which provides a better estimation. Finally, we prove the stability of the quartic functional equation f(2x+y)+f(2x−y)=4f(x+y)+4f(x−y)+24f(x)−6f(y) in random normed spaces. |
| url |
http://dx.doi.org/10.1155/2008/902187 |
| _version_ |
1716801573900779520 |