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Stability of the exponential functional equation in Riesz algebras. (English) Zbl 1474.39068

Summary: We deal with the stability of the exponential Cauchy functional equation \(F(x + y) = F(x) F(y)\) in the class of functions \(F : G \rightarrow L\) 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.

MSC:

39B82 Stability, separation, extension, and related topics for functional equations
39B52 Functional equations for functions with more general domains and/or ranges
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