On Ulam Stability of a Functional Equation in Banach Modules

Abstract

AbstractLet X and Y be Banach spaces and let f : X → Y be an odd mapping. For any rational number r≠2, C. Baak, D. H. Boo, and Th. M. Rassias proved the Hyers–Ulam stability of the functional equationwhere d and l are positive integers so that In this note we solve this equation for arbitrary nonzero scalar r and show that it is actually Hyers–Ulam stable. We thus extend and generalize Baak et al.’s result. Other questions concerning the *-homomorphisms and the multipliers between C*-algebras are also considered.