On the Generalized Hyers-Ulam-Rassias Stability of Quadratic Functional Equations
We achieve the general solution and the generalized Hyers-Ulam-Rassias and Ulam-Gavruta-Rassias stabilities for quadratic functional equations f(ax+by)+f(ax−by)=(b(a+b)/2)f(x+y)+(b(a+b)/2)f(x−y)+(2a2−ab−b2)f(x)+(b2−ab)f(y) where a, b are nonzero fixed integers with b≠±a,−3a, and f(ax+by)+f(ax−by)=2a...
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| Format: | Article |
| Language: | English |
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Wiley
2009-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2009/923476 |
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| author | M. Eshaghi Gordji H. Khodaei |
| author_facet | M. Eshaghi Gordji H. Khodaei |
| author_sort | M. Eshaghi Gordji |
| collection | DOAJ |
| description | We achieve the general solution and the generalized Hyers-Ulam-Rassias and Ulam-Gavruta-Rassias stabilities for quadratic functional equations f(ax+by)+f(ax−by)=(b(a+b)/2)f(x+y)+(b(a+b)/2)f(x−y)+(2a2−ab−b2)f(x)+(b2−ab)f(y) where a, b are nonzero fixed integers with b≠±a,−3a, and f(ax+by)+f(ax−by)=2a2f(x)+2b2f(y) for fixed integers a, b with a,b≠0 and a±b≠0. |
| format | Article |
| id | doaj-art-2fbdc4296fee4ac9a4ec27d06adb71b7 |
| institution | OA Journals |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2009-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-2fbdc4296fee4ac9a4ec27d06adb71b72025-08-20T02:08:11ZengWileyAbstract and Applied Analysis1085-33751687-04092009-01-01200910.1155/2009/923476923476On the Generalized Hyers-Ulam-Rassias Stability of Quadratic Functional EquationsM. Eshaghi Gordji0H. Khodaei1Department of Mathematics, Semnan University, P.O. Box 35195-363, Semnan, IranDepartment of Mathematics, Semnan University, P.O. Box 35195-363, Semnan, IranWe achieve the general solution and the generalized Hyers-Ulam-Rassias and Ulam-Gavruta-Rassias stabilities for quadratic functional equations f(ax+by)+f(ax−by)=(b(a+b)/2)f(x+y)+(b(a+b)/2)f(x−y)+(2a2−ab−b2)f(x)+(b2−ab)f(y) where a, b are nonzero fixed integers with b≠±a,−3a, and f(ax+by)+f(ax−by)=2a2f(x)+2b2f(y) for fixed integers a, b with a,b≠0 and a±b≠0.http://dx.doi.org/10.1155/2009/923476 |
| spellingShingle | M. Eshaghi Gordji H. Khodaei On the Generalized Hyers-Ulam-Rassias Stability of Quadratic Functional Equations Abstract and Applied Analysis |
| title | On the Generalized Hyers-Ulam-Rassias Stability of Quadratic Functional Equations |
| title_full | On the Generalized Hyers-Ulam-Rassias Stability of Quadratic Functional Equations |
| title_fullStr | On the Generalized Hyers-Ulam-Rassias Stability of Quadratic Functional Equations |
| title_full_unstemmed | On the Generalized Hyers-Ulam-Rassias Stability of Quadratic Functional Equations |
| title_short | On the Generalized Hyers-Ulam-Rassias Stability of Quadratic Functional Equations |
| title_sort | on the generalized hyers ulam rassias stability of quadratic functional equations |
| url | http://dx.doi.org/10.1155/2009/923476 |
| work_keys_str_mv | AT meshaghigordji onthegeneralizedhyersulamrassiasstabilityofquadraticfunctionalequations AT hkhodaei onthegeneralizedhyersulamrassiasstabilityofquadraticfunctionalequations |