THE FIXED POINT ALTERNATIVE TO THE STABILITY OF AN ADDITIVE (α, β)-FUNCTIONAL EQUATION.

In this paper, we solve the additive (α, β)-functional equation f(x) + f(y) + 2f(z) = αf(β(x + y +2z)); (0.1) where α, β are fixed real or complex numbers with α ≠4 and αβ= 1. 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 Banach spaces. [ABSTRACT FROM AUTHOR]