Ulam Stability of a Quartic Functional Equation
The oldest quartic functional equation was introduced by J. M. Rassias in (1999), and then was employed by other authors. The functional equation 𝑓(2𝑥+𝑦)+𝑓(2𝑥−𝑦)=4𝑓(𝑥+𝑦)+4𝑓(𝑥−𝑦)+24𝑓(𝑥)−6𝑓(𝑦) is called a quartic functional equation, all of its solution is said to be a quartic function. In the curren...
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2012/232630 |
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| author | Abasalt Bodaghi Idham Arif Alias Mohammad Hosein Ghahramani |
| author_facet | Abasalt Bodaghi Idham Arif Alias Mohammad Hosein Ghahramani |
| author_sort | Abasalt Bodaghi |
| collection | DOAJ |
| description | The oldest quartic functional equation was introduced by J. M. Rassias in (1999), and then was employed by other authors. The functional equation 𝑓(2𝑥+𝑦)+𝑓(2𝑥−𝑦)=4𝑓(𝑥+𝑦)+4𝑓(𝑥−𝑦)+24𝑓(𝑥)−6𝑓(𝑦) is called a quartic functional equation, all of its solution is said to be a quartic function. In the current paper, the Hyers-Ulam stability and the superstability for quartic functional equations are established by using the fixed-point alternative theorem. |
| format | Article |
| id | doaj-art-3b68a79a28564da6a1e7fb01d4640921 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-3b68a79a28564da6a1e7fb01d46409212025-02-03T01:11:43ZengWileyAbstract and Applied Analysis1085-33751687-04092012-01-01201210.1155/2012/232630232630Ulam Stability of a Quartic Functional EquationAbasalt Bodaghi0Idham Arif Alias1Mohammad Hosein Ghahramani2Department of Mathematics, Garmsar Branch, Islamic Azad University, Garmsar, IranInstitute for Mathematical Research, University Putra Malaysia, 43400 UPM, Serdang, Selangor Darul Ehsan, MalaysiaDepartment of Mathematics, Garmsar Branch, Islamic Azad University, Garmsar, IranThe oldest quartic functional equation was introduced by J. M. Rassias in (1999), and then was employed by other authors. The functional equation 𝑓(2𝑥+𝑦)+𝑓(2𝑥−𝑦)=4𝑓(𝑥+𝑦)+4𝑓(𝑥−𝑦)+24𝑓(𝑥)−6𝑓(𝑦) is called a quartic functional equation, all of its solution is said to be a quartic function. In the current paper, the Hyers-Ulam stability and the superstability for quartic functional equations are established by using the fixed-point alternative theorem.http://dx.doi.org/10.1155/2012/232630 |
| spellingShingle | Abasalt Bodaghi Idham Arif Alias Mohammad Hosein Ghahramani Ulam Stability of a Quartic Functional Equation Abstract and Applied Analysis |
| title | Ulam Stability of a Quartic Functional Equation |
| title_full | Ulam Stability of a Quartic Functional Equation |
| title_fullStr | Ulam Stability of a Quartic Functional Equation |
| title_full_unstemmed | Ulam Stability of a Quartic Functional Equation |
| title_short | Ulam Stability of a Quartic Functional Equation |
| title_sort | ulam stability of a quartic functional equation |
| url | http://dx.doi.org/10.1155/2012/232630 |
| work_keys_str_mv | AT abasaltbodaghi ulamstabilityofaquarticfunctionalequation AT idhamarifalias ulamstabilityofaquarticfunctionalequation AT mohammadhoseinghahramani ulamstabilityofaquarticfunctionalequation |