Stability of General Cubic Mapping in Fuzzy Normed Spaces

作者：Javadi S^*; Rassias J M

来源：Analele Stiintifice ale Universitatii Ovidius Constanta, Seria Matematica, 2012, 20(1): 129-149.

• Generalized Hyers-Ulam-Rassias stability
• Cubic functional equation
• Fuzzy normed spaces

We establish some stability results concerning the general cubic functional equation %26lt;br%26gt;f(x + ky) - kf(x + y) + kf(x - y) - f(x - ky) = 2k(k(2) - 1) f(y) %26lt;br%26gt;for fixed k is an element of 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.

• 出版日期2012