Fixed Points in Functional Inequalities

Abstract

Using fixed point methods, we prove the generalized Hyers-Ulam stability of the following functional inequalities vertical bar vertical bar f (x) + f(y) + f(z)vertical bar vertical bar <= vertical bar vertical bar f(x + y + z)vertical bar vertical bar and vertical bar vertical bar f (x) + f(y) + 2f(z)vertical bar vertical bar <= vertical bar vertical bar 2f((x +y)/2 +z)vertical bar vertical bar in the spirit of Th. M. Rassias stability approach.