Stability of Pexider Equations on Semigroup with No Neutral Element
Let S be a commutative semigroup with no neutral element, Y a Banach space, and ℂ the set of complex numbers. In this paper we prove the Hyers-Ulam stability for Pexider equation fx+y-gx-h(y)≤ϵ for all x,y∈S, where f,g,h:S→Y. Using Jung’s theorem we obtain a better bound than that usually obtained....
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2014/153610 |
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| author | Jaeyoung Chung |
| author_facet | Jaeyoung Chung |
| author_sort | Jaeyoung Chung |
| collection | DOAJ |
| description | Let S be a commutative semigroup with no neutral element, Y a Banach space, and ℂ the set of complex numbers. In this paper we prove the Hyers-Ulam stability for Pexider equation fx+y-gx-h(y)≤ϵ for all x,y∈S, where f,g,h:S→Y. Using Jung’s theorem we obtain a better bound than that usually obtained. Also, generalizing the result of Baker (1980) we prove the superstability for Pexider-exponential equation ft+s-gth(s)≤ϵ for all t,s∈S, where f,g,h:S→ℂ. As a direct consequence of the result we also obtain the general solutions of the Pexider-exponential equation ft+s=gth(s) for all t,s∈S, a closed form of which is not yet known. |
| format | Article |
| id | doaj-art-9b89dfdaba61473d9bb3a26502ba1c8c |
| institution | Kabale University |
| issn | 2314-8896 2314-8888 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces |
| spelling | doaj-art-9b89dfdaba61473d9bb3a26502ba1c8c2025-02-03T07:25:21ZengWileyJournal of Function Spaces2314-88962314-88882014-01-01201410.1155/2014/153610153610Stability of Pexider Equations on Semigroup with No Neutral ElementJaeyoung Chung0Department of Mathematics, Kunsan National University, Kunsan 573-701, Republic of KoreaLet S be a commutative semigroup with no neutral element, Y a Banach space, and ℂ the set of complex numbers. In this paper we prove the Hyers-Ulam stability for Pexider equation fx+y-gx-h(y)≤ϵ for all x,y∈S, where f,g,h:S→Y. Using Jung’s theorem we obtain a better bound than that usually obtained. Also, generalizing the result of Baker (1980) we prove the superstability for Pexider-exponential equation ft+s-gth(s)≤ϵ for all t,s∈S, where f,g,h:S→ℂ. As a direct consequence of the result we also obtain the general solutions of the Pexider-exponential equation ft+s=gth(s) for all t,s∈S, a closed form of which is not yet known.http://dx.doi.org/10.1155/2014/153610 |
| spellingShingle | Jaeyoung Chung Stability of Pexider Equations on Semigroup with No Neutral Element Journal of Function Spaces |
| title | Stability of Pexider Equations on Semigroup with No Neutral Element |
| title_full | Stability of Pexider Equations on Semigroup with No Neutral Element |
| title_fullStr | Stability of Pexider Equations on Semigroup with No Neutral Element |
| title_full_unstemmed | Stability of Pexider Equations on Semigroup with No Neutral Element |
| title_short | Stability of Pexider Equations on Semigroup with No Neutral Element |
| title_sort | stability of pexider equations on semigroup with no neutral element |
| url | http://dx.doi.org/10.1155/2014/153610 |
| work_keys_str_mv | AT jaeyoungchung stabilityofpexiderequationsonsemigroupwithnoneutralelement |