Generalized Hyers-Ulam Stability of General Cubic Functional Equation in Random Normed Spaces

Abstract

Random normed spaces provide appropriate tools to study the geometry of nuclear physics and have useful applications in quantum particle physics. In this paper, we investigate the generalized Hyers-Ulam stability of a general cubic functional equation:
f(x + ky)-kf(x + y) + kf(x-y)-f(x-ky) = 2k(k^2-1)f(y)
for fixed k \in \Z^+ with k\ge 2 in random normed spaces
utilizing the direct and fixed point methods.