Functional Inequalities Associated with Jordan‐von Neumann‐Type Additive Functional Equations

Abstract

We prove the generalized Hyers‐Ulam stability of the following functional inequalities: ||f(x)+f(y)+f(z)|| ≤ ||2f((x+y+z)/2)||, ||f(x)+f(y)+f(z)|| ≤ ||f(x+y+z)||, ||f(x)+f(y)+2f(z)|| ≤ ||2f((x+y)/2+z)|| in the spirit of the Rassias stability approach for approximately homomorphisms.