Functional inequalities associated with Jordan-von Neumann-type additive functional equations

Abstract

We prove the generalized Hyers-Ulam stability of the following functional inequalities: parallel to f(x) + f(y)+ f (z)parallel to <= parallel to 2f ((x + y + z)/2)parallel to, f(x)+ f (y)+ f (z)parallel to <= parallel to f(x + y + z)parallel to. parallel to f(x) + f(y) + 2f(z)parallel to <= parallel to 2f((x + y)/2+ z)parallel to in the spirit of the Rassias stability approach for approximately homomorphisms.