Non-Archimedean Hyers-Ulam Stability of an Additive-Quadratic Mapping
Using fixed point method and direct method, we prove the Hyers-Ulam stability of the following additive-quadratic functional equation 𝑟2𝑓((𝑥+𝑦+𝑧)/𝑟)+𝑟2𝑓((𝑥−𝑦+𝑧)/𝑟)+𝑟2𝑓((𝑥+𝑦−𝑧)/𝑟)+𝑟2𝑓((−𝑥+𝑦+𝑧)/𝑟)=4𝑓(𝑥)+4𝑓(𝑦)+4𝑓(𝑧), where 𝑟 is a positive real number, in non-Archimedean normed spaces....
Saved in:
| Main Authors: | , , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2012-01-01
|
| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2012/824257 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832559877268963328 |
|---|---|
| author | Hassan Azadi Kenary Themistocles M. Rassias H. Rezaei S. Talebzadeh Won-Gil Park |
| author_facet | Hassan Azadi Kenary Themistocles M. Rassias H. Rezaei S. Talebzadeh Won-Gil Park |
| author_sort | Hassan Azadi Kenary |
| collection | DOAJ |
| description | Using fixed point method and direct method, we prove the Hyers-Ulam stability of the following additive-quadratic functional equation 𝑟2𝑓((𝑥+𝑦+𝑧)/𝑟)+𝑟2𝑓((𝑥−𝑦+𝑧)/𝑟)+𝑟2𝑓((𝑥+𝑦−𝑧)/𝑟)+𝑟2𝑓((−𝑥+𝑦+𝑧)/𝑟)=4𝑓(𝑥)+4𝑓(𝑦)+4𝑓(𝑧), where 𝑟 is a positive real number, in non-Archimedean normed spaces. |
| format | Article |
| id | doaj-art-03894c4bba0f49f8bc438c390f26195a |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-03894c4bba0f49f8bc438c390f26195a2025-02-03T01:28:58ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2012-01-01201210.1155/2012/824257824257Non-Archimedean Hyers-Ulam Stability of an Additive-Quadratic MappingHassan Azadi Kenary0Themistocles M. Rassias1H. Rezaei2S. Talebzadeh3Won-Gil Park4Department of Mathematics, College of Sciences, Yasouj University, Yasouj 75914-353, IranDepartment of Mathematics, National Technical University of Athens, Zografou Campus, 15780 Athens, GreeceDepartment of Mathematics, College of Sciences, Yasouj University, Yasouj 75914-353, IranDepartment of Mathematics, Islamic Azad University, Firoozabad Branch, Firoozabad, IranDepartment of Mathematics Education, College of Education, Mokwon University, Daejeon 302-729, Republic of KoreaUsing fixed point method and direct method, we prove the Hyers-Ulam stability of the following additive-quadratic functional equation 𝑟2𝑓((𝑥+𝑦+𝑧)/𝑟)+𝑟2𝑓((𝑥−𝑦+𝑧)/𝑟)+𝑟2𝑓((𝑥+𝑦−𝑧)/𝑟)+𝑟2𝑓((−𝑥+𝑦+𝑧)/𝑟)=4𝑓(𝑥)+4𝑓(𝑦)+4𝑓(𝑧), where 𝑟 is a positive real number, in non-Archimedean normed spaces.http://dx.doi.org/10.1155/2012/824257 |
| spellingShingle | Hassan Azadi Kenary Themistocles M. Rassias H. Rezaei S. Talebzadeh Won-Gil Park Non-Archimedean Hyers-Ulam Stability of an Additive-Quadratic Mapping Discrete Dynamics in Nature and Society |
| title | Non-Archimedean Hyers-Ulam Stability of an Additive-Quadratic Mapping |
| title_full | Non-Archimedean Hyers-Ulam Stability of an Additive-Quadratic Mapping |
| title_fullStr | Non-Archimedean Hyers-Ulam Stability of an Additive-Quadratic Mapping |
| title_full_unstemmed | Non-Archimedean Hyers-Ulam Stability of an Additive-Quadratic Mapping |
| title_short | Non-Archimedean Hyers-Ulam Stability of an Additive-Quadratic Mapping |
| title_sort | non archimedean hyers ulam stability of an additive quadratic mapping |
| url | http://dx.doi.org/10.1155/2012/824257 |
| work_keys_str_mv | AT hassanazadikenary nonarchimedeanhyersulamstabilityofanadditivequadraticmapping AT themistoclesmrassias nonarchimedeanhyersulamstabilityofanadditivequadraticmapping AT hrezaei nonarchimedeanhyersulamstabilityofanadditivequadraticmapping AT stalebzadeh nonarchimedeanhyersulamstabilityofanadditivequadraticmapping AT wongilpark nonarchimedeanhyersulamstabilityofanadditivequadraticmapping |