Stability of a Quartic Functional Equation
We obtain the general solution of the generalized quartic functional equation f(x+my)+f(x-my)=2(7m-9)(m-1)f(x)+2m2(m2-1)f(y)-(m-1)2f(2x)+m2{f(x+y) + f(x-y)} for a fixed positive integer m. We prove the Hyers-Ulam stability for this quartic functional equation by the directed method and the fixed poi...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | The Scientific World Journal |
| Online Access: | http://dx.doi.org/10.1155/2014/752146 |
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| author | Abasalt Bodaghi |
| author_facet | Abasalt Bodaghi |
| author_sort | Abasalt Bodaghi |
| collection | DOAJ |
| description | We obtain the general solution of the generalized quartic functional equation f(x+my)+f(x-my)=2(7m-9)(m-1)f(x)+2m2(m2-1)f(y)-(m-1)2f(2x)+m2{f(x+y) + f(x-y)} for a fixed positive integer m. We prove the Hyers-Ulam stability for this quartic functional equation by the directed method and the fixed point method on real Banach spaces. We also investigate the Hyers-Ulam stability for the mentioned quartic functional equation in non-Archimedean spaces. |
| format | Article |
| id | doaj-art-c61387cda95d4fb7be73bf4732acd89f |
| institution | Kabale University |
| issn | 2356-6140 1537-744X |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | The Scientific World Journal |
| spelling | doaj-art-c61387cda95d4fb7be73bf4732acd89f2025-02-03T06:04:42ZengWileyThe Scientific World Journal2356-61401537-744X2014-01-01201410.1155/2014/752146752146Stability of a Quartic Functional EquationAbasalt Bodaghi0Department of Mathematics, Garmsar Branch, Islamic Azad University, Garmsar, IranWe obtain the general solution of the generalized quartic functional equation f(x+my)+f(x-my)=2(7m-9)(m-1)f(x)+2m2(m2-1)f(y)-(m-1)2f(2x)+m2{f(x+y) + f(x-y)} for a fixed positive integer m. We prove the Hyers-Ulam stability for this quartic functional equation by the directed method and the fixed point method on real Banach spaces. We also investigate the Hyers-Ulam stability for the mentioned quartic functional equation in non-Archimedean spaces.http://dx.doi.org/10.1155/2014/752146 |
| spellingShingle | Abasalt Bodaghi Stability of a Quartic Functional Equation The Scientific World Journal |
| title | Stability of a Quartic Functional Equation |
| title_full | Stability of a Quartic Functional Equation |
| title_fullStr | Stability of a Quartic Functional Equation |
| title_full_unstemmed | Stability of a Quartic Functional Equation |
| title_short | Stability of a Quartic Functional Equation |
| title_sort | stability of a quartic functional equation |
| url | http://dx.doi.org/10.1155/2014/752146 |
| work_keys_str_mv | AT abasaltbodaghi stabilityofaquarticfunctionalequation |