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

Yeol Je Cho, Seong Sik Kim, John Michael Rassias, N Hussain


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.

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