Stability of the exponential functional equation in Riesz algebras (Q1725122)

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.