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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Hindawi Limited
2014-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2014/153610 |
| Summary: | 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. |
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| ISSN: | 2314-8896 2314-8888 |