Stability of the Exponential Functional Equation in Riesz Algebras

Abstract

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