Stability of a functional equation in complex banach spaces

Abstract

Using fixed point technique, in the present paper , we wish to examine generalization of the Hyers-Ulam-Rassias stability theorem for the functional equations f ( 2 x + i y ) + f ( x + 2 i y ) = 4 f ( x + i y ) + f ( x ) + f ( y ) (0.1) and f ( 2 x + i y ) − f (i x − 2 y ) = − 4 f (i x − y ) + f ( x ) − f ( − y ) (0.2) in complex Banach spaces .