On a modified Hyers-Ulam stability of homogeneous equation
In this paper, a generalized Hyers-Ulam stability of the homogeneous equation shall be proved, i.e., if a mapping f satisfies the functional inequality ‖f(yx)−ykf(x)‖≤φ(x,y) under suitable conditions, there exists a unique mapping T satisfying T(yx)=ytT(x) and ‖T(x)−f(x)‖≤Φ(x).
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| Main Author: | |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
1998-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1155/S0161171298000672 |
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| _version_ | 1832553277636476928 |
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| author | Soon-Mo Jung |
| author_facet | Soon-Mo Jung |
| author_sort | Soon-Mo Jung |
| collection | DOAJ |
| description | In this paper, a generalized Hyers-Ulam stability of the homogeneous equation shall be
proved, i.e., if a mapping f satisfies the functional inequality ‖f(yx)−ykf(x)‖≤φ(x,y) under suitable
conditions, there exists a unique mapping T
satisfying T(yx)=ytT(x)
and ‖T(x)−f(x)‖≤Φ(x). |
| format | Article |
| id | doaj-art-91d33c1ebc9d4576b8456962953aef0c |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1998-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-91d33c1ebc9d4576b8456962953aef0c2025-02-03T05:54:23ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251998-01-0121347547810.1155/S0161171298000672On a modified Hyers-Ulam stability of homogeneous equationSoon-Mo Jung0Mathematical Part, College of Science & Technology, Hong-Ik University, Chochiwon 339-800, South KoreaIn this paper, a generalized Hyers-Ulam stability of the homogeneous equation shall be proved, i.e., if a mapping f satisfies the functional inequality ‖f(yx)−ykf(x)‖≤φ(x,y) under suitable conditions, there exists a unique mapping T satisfying T(yx)=ytT(x) and ‖T(x)−f(x)‖≤Φ(x).http://dx.doi.org/10.1155/S0161171298000672Functional equationhomogeneous equationstability. |
| spellingShingle | Soon-Mo Jung On a modified Hyers-Ulam stability of homogeneous equation International Journal of Mathematics and Mathematical Sciences Functional equation homogeneous equation stability. |
| title | On a modified Hyers-Ulam stability of homogeneous equation |
| title_full | On a modified Hyers-Ulam stability of homogeneous equation |
| title_fullStr | On a modified Hyers-Ulam stability of homogeneous equation |
| title_full_unstemmed | On a modified Hyers-Ulam stability of homogeneous equation |
| title_short | On a modified Hyers-Ulam stability of homogeneous equation |
| title_sort | on a modified hyers ulam stability of homogeneous equation |
| topic | Functional equation homogeneous equation stability. |
| url | http://dx.doi.org/10.1155/S0161171298000672 |
| work_keys_str_mv | AT soonmojung onamodifiedhyersulamstabilityofhomogeneousequation |