Stability of the Exponential Functional Equation in Riesz Algebras. (5th January 2014) - Batko, Bogdan
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.