Fixed Points and Quadratic rho-Functional Inequalities in Banach 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(4f(x+y/2) + f(x - y) - 2f(x) - 2f(y))parallel to,

where rho is a fixed number with vertical bar rho vertical bar < 1, and

parallel to 4f(x + y/2) + f(x - y) - 2f(x) - 2f(y)parallel to <= parallel to rho(f(x + y) + f(x - y) - 2f(x) -2f(y))parallel to,

where rho is a fixed number with vertical bar rho vertical bar < 1/2. Using the fixed point method, we prove the Hyers-Ulam stability of the above quadratic rho-functional inequalities in complex Banach spaces.