stability of pexider equations on semigroup with no neutral element
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ID: 172658
2014
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Abstract
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.
| Reference Key |
chung2014journalstability
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|---|---|
| Authors | ;Jaeyoung Chung |
| Journal | Biosensors |
| Year | 2014 |
| DOI |
10.1155/2014/153610
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