A Linear Functional Equation of Third Order Associated with the Fibonacci Numbers
Given a vector space X, we investigate the solutions f:R→X of the linear functional equation of third order fx=pfx-1+qfx-2+rf(x-3), which is strongly associated with a well-known identity for the Fibonacci numbers. Moreover, we prove the Hyers-Ulam stability of that equation.
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/137468 |
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| _version_ | 1849404095143608320 |
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| author | Soon-Mo Jung Michael Th. Rassias |
| author_facet | Soon-Mo Jung Michael Th. Rassias |
| author_sort | Soon-Mo Jung |
| collection | DOAJ |
| description | Given a vector space X, we investigate the solutions f:R→X of the linear functional equation of third order fx=pfx-1+qfx-2+rf(x-3), which is strongly associated with a well-known identity for the Fibonacci numbers. Moreover, we prove the Hyers-Ulam stability of that equation. |
| format | Article |
| id | doaj-art-91b17ef76ecb4e3d965ed0c4d7613998 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-91b17ef76ecb4e3d965ed0c4d76139982025-08-20T03:37:06ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/137468137468A Linear Functional Equation of Third Order Associated with the Fibonacci NumbersSoon-Mo Jung0Michael Th. Rassias1Mathematics Section, College of Science and Technology, Hongik University, Sejong 339-701, Republic of KoreaDepartment of Mathematics, ETH-Zürich, Ramistraße 101, 8092 Zürich, SwitzerlandGiven a vector space X, we investigate the solutions f:R→X of the linear functional equation of third order fx=pfx-1+qfx-2+rf(x-3), which is strongly associated with a well-known identity for the Fibonacci numbers. Moreover, we prove the Hyers-Ulam stability of that equation.http://dx.doi.org/10.1155/2014/137468 |
| spellingShingle | Soon-Mo Jung Michael Th. Rassias A Linear Functional Equation of Third Order Associated with the Fibonacci Numbers Abstract and Applied Analysis |
| title | A Linear Functional Equation of Third Order Associated with the Fibonacci Numbers |
| title_full | A Linear Functional Equation of Third Order Associated with the Fibonacci Numbers |
| title_fullStr | A Linear Functional Equation of Third Order Associated with the Fibonacci Numbers |
| title_full_unstemmed | A Linear Functional Equation of Third Order Associated with the Fibonacci Numbers |
| title_short | A Linear Functional Equation of Third Order Associated with the Fibonacci Numbers |
| title_sort | linear functional equation of third order associated with the fibonacci numbers |
| url | http://dx.doi.org/10.1155/2014/137468 |
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