Approximately Quadratic Mappings on Restricted Domains
<p/> <p>We introduce a generalized quadratic functional equation <inline-formula> <graphic file="1029-242X-2010-503458-i1.gif"/></inline-formula>, where <inline-formula> <graphic file="1029-242X-2010-503458-i2.gif"/></inline-formula>...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2010-01-01
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| Series: | Journal of Inequalities and Applications |
| Online Access: | http://www.journalofinequalitiesandapplications.com/content/2010/503458 |
| Summary: | <p/> <p>We introduce a generalized quadratic functional equation <inline-formula> <graphic file="1029-242X-2010-503458-i1.gif"/></inline-formula>, where <inline-formula> <graphic file="1029-242X-2010-503458-i2.gif"/></inline-formula>, <inline-formula> <graphic file="1029-242X-2010-503458-i3.gif"/></inline-formula> are nonzero real numbers with <inline-formula> <graphic file="1029-242X-2010-503458-i4.gif"/></inline-formula>. We show that this functional equation is quadratic if <inline-formula> <graphic file="1029-242X-2010-503458-i5.gif"/></inline-formula>, <inline-formula> <graphic file="1029-242X-2010-503458-i6.gif"/></inline-formula> are rational numbers. We also investigate its stability problem on restricted domains. These results are applied to study of an asymptotic behavior of these generalized quadratic mappings.</p> |
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| ISSN: | 1025-5834 1029-242X |