Investigation of the Stability via Shadowing Property
<p/> <p>The shadowing property is to find an exact solution to an iterated map that remains close to an approximate solution. In this article, using shadowing property, we show the stability of the following equation in normed group: <inline-formula> <graphic file="1029-242...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2009-01-01
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| Series: | Journal of Inequalities and Applications |
| Online Access: | http://www.journalofinequalitiesandapplications.com/content/2009/156167 |
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doaj-0bc95ab50fad4533b622f4e94498fd1f2020-11-25T02:51:26ZengSpringerOpenJournal of Inequalities and Applications1025-58341029-242X2009-01-0120091156167Investigation of the Stability via Shadowing PropertyKoh HeejeongKu Se-HyunLee Sang-Hyuk<p/> <p>The shadowing property is to find an exact solution to an iterated map that remains close to an approximate solution. In this article, using shadowing property, we show the stability of the following equation in normed group: <inline-formula> <graphic file="1029-242X-2009-156167-i1.gif"/></inline-formula>, where <inline-formula> <graphic file="1029-242X-2009-156167-i2.gif"/></inline-formula>, <inline-formula> <graphic file="1029-242X-2009-156167-i3.gif"/></inline-formula> and <inline-formula> <graphic file="1029-242X-2009-156167-i4.gif"/></inline-formula> is a mapping. And we prove that the even mapping which satisfies the above equation is quadratic and also the Hyers-Ulam stability of the functional equation in Banach spaces.</p>http://www.journalofinequalitiesandapplications.com/content/2009/156167 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Koh Heejeong Ku Se-Hyun Lee Sang-Hyuk |
| spellingShingle |
Koh Heejeong Ku Se-Hyun Lee Sang-Hyuk Investigation of the Stability via Shadowing Property Journal of Inequalities and Applications |
| author_facet |
Koh Heejeong Ku Se-Hyun Lee Sang-Hyuk |
| author_sort |
Koh Heejeong |
| title |
Investigation of the Stability via Shadowing Property |
| title_short |
Investigation of the Stability via Shadowing Property |
| title_full |
Investigation of the Stability via Shadowing Property |
| title_fullStr |
Investigation of the Stability via Shadowing Property |
| title_full_unstemmed |
Investigation of the Stability via Shadowing Property |
| title_sort |
investigation of the stability via shadowing property |
| publisher |
SpringerOpen |
| series |
Journal of Inequalities and Applications |
| issn |
1025-5834 1029-242X |
| publishDate |
2009-01-01 |
| description |
<p/> <p>The shadowing property is to find an exact solution to an iterated map that remains close to an approximate solution. In this article, using shadowing property, we show the stability of the following equation in normed group: <inline-formula> <graphic file="1029-242X-2009-156167-i1.gif"/></inline-formula>, where <inline-formula> <graphic file="1029-242X-2009-156167-i2.gif"/></inline-formula>, <inline-formula> <graphic file="1029-242X-2009-156167-i3.gif"/></inline-formula> and <inline-formula> <graphic file="1029-242X-2009-156167-i4.gif"/></inline-formula> is a mapping. And we prove that the even mapping which satisfies the above equation is quadratic and also the Hyers-Ulam stability of the functional equation in Banach spaces.</p> |
| url |
http://www.journalofinequalitiesandapplications.com/content/2009/156167 |
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AT kohheejeong investigationofthestabilityviashadowingproperty AT kusehyun investigationofthestabilityviashadowingproperty AT leesanghyuk investigationofthestabilityviashadowingproperty |
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