CUBIC ρ-FUNCTIONAL INEQUALITY AND QUARTIC ρ-FUNCTIONAL INEQUALITY.

In this paper, we solve the following cubic p-functional inequality Il f (2x + y) + f (2x - y) - 2f (x + y) - 2f (x - y) - 12f (x)|| where p is a fixed complex number with | ρ| < 2, and the quartic ρ-functional inequality ||f (2x + y) + f (2x - y) - 4 f (x + y) - 4f (x - y) - 24f (x) + 6f(y)||... where ρ is a fixed complex number with | ρ| < 2. Using the direct method, we prove the Hyers-Ulam stability of the cubic ρ-functional inequality (0.1) and the quartic ρ-functional inequality (0.2) in complex Banach spaces. [ABSTRACT FROM AUTHOR]