On the Stability of Additive, Quadratic, Cubic and Quartic Set-valued Functional Equations

For m = 1, 2, 3, 4, we study the following set-valued functional equation f(ax + y) circle plus f(ax - y) = a(m-2) [f(x + y) circle plus f(x - y)] circle plus 2(a(2) - 1) [a(m-2) f(x) circle plus (m - 2)(1 - (m - 2)(2))/6 f(y)] where a is a fixed positive integer with a > 1. We also prove the stability of this set-valued functional equation by using the Banach fixed point theorem.