Quadratic rho-functional inequalities in normed spaces

Abstract

In this paper, we solve the quadratic rho-functional inequalities parallel to f(x + y) + f(x - y) - 2f(x) - 2f(y)parallel to <= parallel to rho(2f(x+y)/2 + 2f(x - y)/2 - f(x) - f(y)parallel to, <=parallel to rho(f(x + y) + f(x - y) - 2f(x) - 2f(y))parallel to, where rho is a number with broken vertical bar p broken vertical bar < 1/2. Using the fixed point method, we prove the Hyers-Ulam stability of the quadratic rho is a functional inequalities (0.1) and (0.2) in normed spaces.