Equivalence for Various Forms of Quadratic Functional Equations and Their Generalized Hyers–Ulam–Rassias Stability
In this manuscript, we study the properties and equivalence results for different forms of quadratic functional equations. Using the Brzdȩk and Ciepliński fixed-point approach, we investigate the generalized Hyers–Ulam–Rassias stability for the 3-variables quadratic functional equation in the settin...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Hindawi Limited
2023-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2023/1721273 |
| _version_ | 1797850975923339264 |
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| author | Ravinder Kumar Sharma Sumit Chandok |
| author_facet | Ravinder Kumar Sharma Sumit Chandok |
| author_sort | Ravinder Kumar Sharma |
| collection | DOAJ |
| description | In this manuscript, we study the properties and equivalence results for different forms of quadratic functional equations. Using the Brzdȩk and Ciepliński fixed-point approach, we investigate the generalized Hyers–Ulam–Rassias stability for the 3-variables quadratic functional equation in the setting of 2-Banach space. Also, we obtain some hyperstability results for the 3-variables quadratic functional equation. The results obtained in this paper extend several known results of the literature to the setting of 2-Banach space. |
| first_indexed | 2024-04-09T19:10:17Z |
| format | Article |
| id | doaj.art-78ad8fad575c488aa0cf909aa351d9bd |
| institution | Directory Open Access Journal |
| issn | 1687-0425 |
| language | English |
| last_indexed | 2024-04-09T19:10:17Z |
| publishDate | 2023-01-01 |
| publisher | Hindawi Limited |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj.art-78ad8fad575c488aa0cf909aa351d9bd2023-04-07T00:00:06ZengHindawi LimitedInternational Journal of Mathematics and Mathematical Sciences1687-04252023-01-01202310.1155/2023/1721273Equivalence for Various Forms of Quadratic Functional Equations and Their Generalized Hyers–Ulam–Rassias StabilityRavinder Kumar Sharma0Sumit Chandok1School of MathematicsSchool of MathematicsIn this manuscript, we study the properties and equivalence results for different forms of quadratic functional equations. Using the Brzdȩk and Ciepliński fixed-point approach, we investigate the generalized Hyers–Ulam–Rassias stability for the 3-variables quadratic functional equation in the setting of 2-Banach space. Also, we obtain some hyperstability results for the 3-variables quadratic functional equation. The results obtained in this paper extend several known results of the literature to the setting of 2-Banach space.http://dx.doi.org/10.1155/2023/1721273 |
| spellingShingle | Ravinder Kumar Sharma Sumit Chandok Equivalence for Various Forms of Quadratic Functional Equations and Their Generalized Hyers–Ulam–Rassias Stability International Journal of Mathematics and Mathematical Sciences |
| title | Equivalence for Various Forms of Quadratic Functional Equations and Their Generalized Hyers–Ulam–Rassias Stability |
| title_full | Equivalence for Various Forms of Quadratic Functional Equations and Their Generalized Hyers–Ulam–Rassias Stability |
| title_fullStr | Equivalence for Various Forms of Quadratic Functional Equations and Their Generalized Hyers–Ulam–Rassias Stability |
| title_full_unstemmed | Equivalence for Various Forms of Quadratic Functional Equations and Their Generalized Hyers–Ulam–Rassias Stability |
| title_short | Equivalence for Various Forms of Quadratic Functional Equations and Their Generalized Hyers–Ulam–Rassias Stability |
| title_sort | equivalence for various forms of quadratic functional equations and their generalized hyers ulam rassias stability |
| url | http://dx.doi.org/10.1155/2023/1721273 |
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