QUADRATIC rho-FUNCTIONAL INEQUALITIES IN BANACH SPACES: A FIXED POINT APPROACH

Abstract

In this paper, we solve the following quadratic rho-functional inequalities parallel to f (x+y+z/2) + f (x-y-z/2) + f(y-x-z/2) + f (z-x-y/2) - f (x) - f (y) - f (z) parallel to (0.1) <= parallel to rho(f (x+y+x) + f (x-y-z) + f (y-x-z) +f (z-x-y) - 4f (x) - 4f (y) - 4f(z)) parallel to, where rho is a fi xed complex number with |rho| < 1/8, and parallel to rho(f (x+y+x) + f (x-y-z) + f (y-x-z) +f (z-x-y) - 4f (x) - 4f (y) - 4f(z)) parallel to (0.2) <= parallel to f (x+y+z/2) + f (x-y-z/2) + f(y-x-z/2) + f (z-x-y/2) - f (x) - f (y) - f (z) parallel to, where rho is a fixed complex number with |rho| < 4. Using the fixed point method, we prove the Hyers-Ulam stability of the quadratic rho-functional inequalities (0.1) and (0.2) in complex Banach spaces.