The Jensen functional equation in non-Archimedean normed spaces
We investigate the Hyers–Ulam–Rassias stability of the Jensen functional equation in non-Archimedean normed spaces and study its asymptotic behavior in two directions: bounded and unbounded Jensen differences. In particular, we show that a mapping f between non-Archimedean spaces with f(0)=0 is addi...
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| Format: | Article |
| Language: | English |
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Wiley
2009-01-01
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| Series: | Journal of Function Spaces and Applications |
| Online Access: | http://dx.doi.org/10.1155/2009/802032 |
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| _version_ | 1832560999896449024 |
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| author | Mohammad Sal Moslehian |
| author_facet | Mohammad Sal Moslehian |
| author_sort | Mohammad Sal Moslehian |
| collection | DOAJ |
| description | We investigate the Hyers–Ulam–Rassias stability of the Jensen
functional equation in non-Archimedean normed spaces and study its asymptotic
behavior in two directions: bounded and unbounded Jensen differences. In
particular, we show that a mapping f between non-Archimedean spaces with
f(0)=0 is additive if and only if ‖f(x+y2)−f(x)+f(y)2‖→0 as max {‖x‖,‖y‖}→∞. |
| format | Article |
| id | doaj-art-1b84a5e4ad0f4d67b7f42c2ed2dc48a9 |
| institution | Kabale University |
| issn | 0972-6802 |
| language | English |
| publishDate | 2009-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces and Applications |
| spelling | doaj-art-1b84a5e4ad0f4d67b7f42c2ed2dc48a92025-02-03T01:26:06ZengWileyJournal of Function Spaces and Applications0972-68022009-01-0171132410.1155/2009/802032The Jensen functional equation in non-Archimedean normed spacesMohammad Sal Moslehian0Department of Pure Mathematics, Ferdowsi University of Mashhad, P. O. Box, 1159, Mashhad 91775, IranWe investigate the Hyers–Ulam–Rassias stability of the Jensen functional equation in non-Archimedean normed spaces and study its asymptotic behavior in two directions: bounded and unbounded Jensen differences. In particular, we show that a mapping f between non-Archimedean spaces with f(0)=0 is additive if and only if ‖f(x+y2)−f(x)+f(y)2‖→0 as max {‖x‖,‖y‖}→∞.http://dx.doi.org/10.1155/2009/802032 |
| spellingShingle | Mohammad Sal Moslehian The Jensen functional equation in non-Archimedean normed spaces Journal of Function Spaces and Applications |
| title | The Jensen functional equation in non-Archimedean normed spaces |
| title_full | The Jensen functional equation in non-Archimedean normed spaces |
| title_fullStr | The Jensen functional equation in non-Archimedean normed spaces |
| title_full_unstemmed | The Jensen functional equation in non-Archimedean normed spaces |
| title_short | The Jensen functional equation in non-Archimedean normed spaces |
| title_sort | jensen functional equation in non archimedean normed spaces |
| url | http://dx.doi.org/10.1155/2009/802032 |
| work_keys_str_mv | AT mohammadsalmoslehian thejensenfunctionalequationinnonarchimedeannormedspaces AT mohammadsalmoslehian jensenfunctionalequationinnonarchimedeannormedspaces |