Stability of General Cubic Mapping in Fuzzy Normed Spaces

S. Javadi, J. M. Rassias
2012 Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica  
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
doi:10.2478/v10309-012-0010-y fatcat:v2tv53k44zbtphnhwpk7ujyghy