AN ADDITIVE (α, β)-FUNCTIONAL EQUATION AND LINEAR MAPPINGS IN BANACH SPACES.

In this paper, we investigate the additive (α β)-functional equation f(x) + αf(αy) = β-1f(β(x + y)) for all complex numbers α with ¦α¦ = 1 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 (α, β)-functional equation (0.1) in complex Banach spaces. [ABSTRACT FROM AUTHOR]