QUADRATIC ρ-FUNCTIONAL EQUATIONS.

In this paper, we solve the quadratic ρ-functional equations f(x + y) + f(x - y) - 2f(x) - 2f(y) (0.1) = ρ ( 2f ( x + y/2 ) + 2f ( x - y/2 ) - f(x) - f(y)), where ρ is a fixed non-Archimedean number or a fixed real or complex number with ρ ≠ -1, 2, and 2f ( x + y/2 ) + 2f ( x - y/2 ) - f(x) - f(y) (0.2) = ρ(f(x + y) + f(x - y) - 2f(x) - 2f(y)), whereρ is a fixed non-Archimedean number or a fixed real or complex number with ρ ≠ -1; 1/2 . Using the direct method, we prove the Hyers-Ulam stability of the quadratic ρ-functional equations (0.1) and (0.2) in non-Archimedean Banach spaces and in Banach spaces. [ABSTRACT FROM AUTHOR]