Stability of the Exponential Functional Equation in Riesz Algebras

Bogdan Batko

Abstract and Applied Analysis, 2014, vol. 2014, issue 1

Abstract: 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.

Date: 2014
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https://doi.org/10.1155/2014/848540

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:848540

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