On the Generalized Ulam-Gavruta-Rassias Stability of Mixed-Type Linear and Euler-Lagrange-Rassias Functional Equations
In this paper, the mixed-type linear and Euler-Lagrange-Rassias functional equations introduced by J. M. Rassias is generalized to the following n-dimensional functional equation: f(∑i=1nxi)+(n−2)∑i=1nf(xi)=∑1≤i<j≤nf(xi−xj) when n>2. We prove the general solutions and investigate its general...
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| Format: | Article |
| Language: | English |
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Wiley
2007-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2007/63239 |
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| _version_ | 1832560723053510656 |
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| author | Paisan Nakmahachalasint |
| author_facet | Paisan Nakmahachalasint |
| author_sort | Paisan Nakmahachalasint |
| collection | DOAJ |
| description | In this paper, the mixed-type linear and Euler-Lagrange-Rassias
functional equations introduced by J. M. Rassias is generalized to the
following
n-dimensional functional equation:
f(∑i=1nxi)+(n−2)∑i=1nf(xi)=∑1≤i<j≤nf(xi−xj) when n>2. We prove the general solutions and investigate its generalized
Ulam-Gavruta-Rassias stability. |
| format | Article |
| id | doaj-art-304452ffb1ff42b29268964375ff77ed |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2007-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-304452ffb1ff42b29268964375ff77ed2025-02-03T01:26:47ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252007-01-01200710.1155/2007/6323963239On the Generalized Ulam-Gavruta-Rassias Stability of Mixed-Type Linear and Euler-Lagrange-Rassias Functional EquationsPaisan Nakmahachalasint0Department of Mathematics, Faculty of Science, Chulalongkorn University, Bangkok 10330, ThailandIn this paper, the mixed-type linear and Euler-Lagrange-Rassias functional equations introduced by J. M. Rassias is generalized to the following n-dimensional functional equation: f(∑i=1nxi)+(n−2)∑i=1nf(xi)=∑1≤i<j≤nf(xi−xj) when n>2. We prove the general solutions and investigate its generalized Ulam-Gavruta-Rassias stability.http://dx.doi.org/10.1155/2007/63239 |
| spellingShingle | Paisan Nakmahachalasint On the Generalized Ulam-Gavruta-Rassias Stability of Mixed-Type Linear and Euler-Lagrange-Rassias Functional Equations International Journal of Mathematics and Mathematical Sciences |
| title | On the Generalized Ulam-Gavruta-Rassias Stability of Mixed-Type Linear and Euler-Lagrange-Rassias Functional Equations |
| title_full | On the Generalized Ulam-Gavruta-Rassias Stability of Mixed-Type Linear and Euler-Lagrange-Rassias Functional Equations |
| title_fullStr | On the Generalized Ulam-Gavruta-Rassias Stability of Mixed-Type Linear and Euler-Lagrange-Rassias Functional Equations |
| title_full_unstemmed | On the Generalized Ulam-Gavruta-Rassias Stability of Mixed-Type Linear and Euler-Lagrange-Rassias Functional Equations |
| title_short | On the Generalized Ulam-Gavruta-Rassias Stability of Mixed-Type Linear and Euler-Lagrange-Rassias Functional Equations |
| title_sort | on the generalized ulam gavruta rassias stability of mixed type linear and euler lagrange rassias functional equations |
| url | http://dx.doi.org/10.1155/2007/63239 |
| work_keys_str_mv | AT paisannakmahachalasint onthegeneralizedulamgavrutarassiasstabilityofmixedtypelinearandeulerlagrangerassiasfunctionalequations |