Hyers–Ulam stability; additive ( α,β )-functional equation; C -linear mapping; fixed point method; direct method; complex Banach space
SPRINGER BASEL AG
JOURNAL OF FIXED POINT THEORY AND APPLICATIONS, v. 18, NO. 3, Page. 495-504
In this paper, we investigate the additive ( α,β )-functional equation f(x+y)+α¯f(αz)=β−1f(β(x+y+z)) 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 this additive ( α,β )-functional equation in complex Banach spaces.