Stability of generalized additive Cauchy equations
A familiar functional equation f(ax+b)=cf(x) will be solved in the class of functions f:ℝ→ℝ. Applying this result we will investigate the Hyers-Ulam-Rassias stability problem of the generalized additive Cauchy equation f(a1x1+⋯+amxm+x0)=∑i=1mbif(ai1x1+⋯+aimxm) in connection with the question of Rass...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Wiley
2000-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1155/S0161171200005184 |
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| _version_ | 1832563926852698112 |
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| author | Soon-Mo Jung Ki-Suk Lee |
| author_facet | Soon-Mo Jung Ki-Suk Lee |
| author_sort | Soon-Mo Jung |
| collection | DOAJ |
| description | A familiar functional equation f(ax+b)=cf(x) will be solved in
the class of functions f:ℝ→ℝ. Applying this result
we will investigate the Hyers-Ulam-Rassias stability problem of the
generalized additive Cauchy equation
f(a1x1+⋯+amxm+x0)=∑i=1mbif(ai1x1+⋯+aimxm) in connection with the question of Rassias and Tabor. |
| format | Article |
| id | doaj-art-8570d60b11284861b50cd95ff8ee4f7f |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2000-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-8570d60b11284861b50cd95ff8ee4f7f2025-02-03T01:12:10ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252000-01-01241172172710.1155/S0161171200005184Stability of generalized additive Cauchy equationsSoon-Mo Jung0Ki-Suk Lee1Mathematics Section, College of Science and Technology, Hong-Ik University, Chochiwon 339-701, KoreaDepartment of Mathematics Education, Korea National University of Education, Choongbook, Chongwon 363-791, KoreaA familiar functional equation f(ax+b)=cf(x) will be solved in the class of functions f:ℝ→ℝ. Applying this result we will investigate the Hyers-Ulam-Rassias stability problem of the generalized additive Cauchy equation f(a1x1+⋯+amxm+x0)=∑i=1mbif(ai1x1+⋯+aimxm) in connection with the question of Rassias and Tabor.http://dx.doi.org/10.1155/S0161171200005184Generalized additive Cauchy equationHyers-Ulam-Rassias stability. |
| spellingShingle | Soon-Mo Jung Ki-Suk Lee Stability of generalized additive Cauchy equations International Journal of Mathematics and Mathematical Sciences Generalized additive Cauchy equation Hyers-Ulam-Rassias stability. |
| title | Stability of generalized additive Cauchy equations |
| title_full | Stability of generalized additive Cauchy equations |
| title_fullStr | Stability of generalized additive Cauchy equations |
| title_full_unstemmed | Stability of generalized additive Cauchy equations |
| title_short | Stability of generalized additive Cauchy equations |
| title_sort | stability of generalized additive cauchy equations |
| topic | Generalized additive Cauchy equation Hyers-Ulam-Rassias stability. |
| url | http://dx.doi.org/10.1155/S0161171200005184 |
| work_keys_str_mv | AT soonmojung stabilityofgeneralizedadditivecauchyequations AT kisuklee stabilityofgeneralizedadditivecauchyequations |