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.


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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