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 |
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| Language: | English |
| Published: |
SpringerOpen
2009-02-01
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| Series: | Journal of Inequalities and Applications |
| Online Access: | http://dx.doi.org/10.1155/2008/902187 |
| Summary: | 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. |
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| ISSN: | 1025-5834 1029-242X |