AN ADDITIVE (U, β)-FUNCTIONAL EQUATION AND MODULE LINEAR MAPPINGS

Abstract

Let A be a unital C^∗ -algebra. In this paper, we investigate the additive (u,β)- functional equation:

f(x) + u^∗ f(uy) = β^{−1} f(β(x + y))

for all unitary elements u in A and for a fixed nonzero complex number β. Using the fixed point method and the direct method, we prove the Hyers-Ulam stability of the additive (u,β)-functional equation in Banach modules.