Published Online: May 17, 2013
Page range: 129 - 150
DOI: https://doi.org/10.2478/v10309-012-0010-y
Keywords
This content is open access.
We establish some stability results concerning the general cubic functional equation
f(x + ky) - kf(x + y) + kf(x - y) - f(x - ky) = 2k(k2 - 1)f(y)
for fixed k ℕ\{1} in the fuzzy normed spaces. More precisely, we show under some suitable conditions that an approximately cubic function can be approximated by a cubic mapping in a fuzzy sense and we establish that the existence of a solution for any approximately cubic mapping guarantees the completeness of the fuzzy normed spaces