Stability of the Exponential Functional Equation in Riesz Algebras
We deal with the stability of the exponential Cauchy functional equation F(x+y)=F(x)F(y) in the class of functions F:G→L mapping a group (G, +) into a Riesz algebra L. The main aim of this paper is to prove that the exponential Cauchy functional equation is stable in the sense of Hyers-Ulam and is n...
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| Format: | Article |
| Language: | English |
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Hindawi Limited
2014-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/848540 |
| Summary: | We deal with the stability of the exponential Cauchy functional equation F(x+y)=F(x)F(y) in the class of functions F:G→L mapping a group (G, +) into a Riesz algebra L. The main aim of this paper is to prove that the exponential Cauchy functional equation is stable in the sense of Hyers-Ulam and is not superstable in the sense of Baker. To prove the stability we use the Yosida Spectral Representation Theorem. |
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| ISSN: | 1085-3375 1687-0409 |