On the hyperstablity of a functional equation in commutative groups

Abstract

Using the fixed point method, we prove the hyperstablity of the functional equation f (ax + by) = (a 2 + b)/2 f (x + y) + (a - b)/2 f (x - y), where a, b are different integers greater than 1, in the class of functions from a commutative group into a commutative complete metric group.