Additive ρ-functional inequalities in normed spaces

Abstract

In this paper, we solve the additive rho-functional inequalities

parallel to f(x + y) - f(x) - f(y) parallel to <= parallel to rho(2f (x + y/2) - f(x) - f(y) parallel to (1)

and

parallel to 2f (x + y)/2) - f(x) - f(y) parallel to <= parallel to rho(f (x + y) - f(x) - f(y)) parallel to, (2)

where rho is a number with vertical bar rho vertical bar < 1. Using the fixed point method, we prove the Hyers-Ulam stability of the additive functional inequalities (1) and (2) in normed spaces.