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

• Record Type: Journal Article
• Authors: Batko, Bogdan
• Other Names: Banaś Józef Academic Editor.
• Is Part Of: Abstract and applied analysis. Volume 2014(2014)
• Publication Date: 2014-01-05
• Subjects: Mathematical analysis -- Periodicals; Mathematical analysis; Applied Mathematics; Mathematical Analysis; Periodicals; 515.05
• DOI: 10.1155/2014/848540
• Languages: English
• ISSNs: 1085-3375

Abstract

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.