3-Variable double ρ-functional inequalities of Drygas

Abstract

Drygas introduced the functional equation f (x + y) + f (x - y) =2f(x) + f(y) + f(-y) in quasi-inner product spaces. In this paper, we introduce and solve 3-variable double rho-functional inequalities associated to the functional equation f (x + y + z)+ f (x + y-z) = 2f(x) + 2f (y) + f (z) + f(-z). Moreover, we prove the Hyers-Ulam stability of the 3-variable double rho-functional inequalities in complex Banach spaces.