-Fuzzy stability of cubic functional equations !()
1 Department of Mathematics, Texas A&M University - Kingsville, Kingsville, TX 78363, USA
2 Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia
3 Department of Mathematics Education and the RINS, Gyeongsang National University, Chinju 660-701, Korea
4 Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, I.R. Iran
5 Department of Mathematics and Physics, North China Electric Power University, Baoding 071003, China
Journal of Inequalities and Applications 2012, 2012:77 doi:10.1186/1029-242X-2012-77Published: 2 April 2012
We establish some stability results for the cubic functional equations
in the setting of various -fuzzy normed spaces that in turn generalize a Hyers-Ulam stability result in the framework of classical normed spaces. First, we shall prove the stability of cubic functional equations in the -fuzzy normed space under arbitrary t-norm which generalizes previous studies. Then, we prove the stability of cubic functional equations in the non-Archimedean -fuzzy normed space. We therefore provide a link among different disciplines: fuzzy set theory, lattice theory, non-Archimedean spaces, and mathematical analysis.
Mathematics Subject Classification (2000): Primary 54E40; Secondary 39B82, 46S50, 46S40.