On Ulam's Type Stability of the Cauchy Additive Equation
We prove a general result on Ulam's type stability of the functional equation fx+y=fx+fy, in the class of functions mapping a commutative group into a commutative group. As a consequence, we deduce from it some hyperstability outcomes. Moreover, we also show how to use that result to improve so...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | The Scientific World Journal |
| Online Access: | http://dx.doi.org/10.1155/2014/540164 |
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| _version_ | 1832559847380353024 |
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| author | Janusz Brzdęk |
| author_facet | Janusz Brzdęk |
| author_sort | Janusz Brzdęk |
| collection | DOAJ |
| description | We prove a general result on Ulam's type stability of the functional equation fx+y=fx+fy, in the class of functions mapping a commutative group into a commutative group. As a consequence, we deduce from it some hyperstability outcomes. Moreover, we also show how to use that result to improve some earlier stability estimations given by Isaac and Rassias. |
| format | Article |
| id | doaj-art-9cb0dfa8596640578c037f1544f051a5 |
| institution | Kabale University |
| issn | 2356-6140 1537-744X |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | The Scientific World Journal |
| spelling | doaj-art-9cb0dfa8596640578c037f1544f051a52025-02-03T01:29:01ZengWileyThe Scientific World Journal2356-61401537-744X2014-01-01201410.1155/2014/540164540164On Ulam's Type Stability of the Cauchy Additive EquationJanusz Brzdęk0Department of Mathematics, Pedagogical University, Podchorążych 2, 30-084 Kraków, PolandWe prove a general result on Ulam's type stability of the functional equation fx+y=fx+fy, in the class of functions mapping a commutative group into a commutative group. As a consequence, we deduce from it some hyperstability outcomes. Moreover, we also show how to use that result to improve some earlier stability estimations given by Isaac and Rassias.http://dx.doi.org/10.1155/2014/540164 |
| spellingShingle | Janusz Brzdęk On Ulam's Type Stability of the Cauchy Additive Equation The Scientific World Journal |
| title | On Ulam's Type Stability of the Cauchy Additive Equation |
| title_full | On Ulam's Type Stability of the Cauchy Additive Equation |
| title_fullStr | On Ulam's Type Stability of the Cauchy Additive Equation |
| title_full_unstemmed | On Ulam's Type Stability of the Cauchy Additive Equation |
| title_short | On Ulam's Type Stability of the Cauchy Additive Equation |
| title_sort | on ulam s type stability of the cauchy additive equation |
| url | http://dx.doi.org/10.1155/2014/540164 |
| work_keys_str_mv | AT januszbrzdek onulamstypestabilityofthecauchyadditiveequation |