Fuzzy stability of the Jensen functional equation

نویسندگان

  • Alireza Kamel Mirmostafaee
  • M. Mirzavaziri
  • Mohammad Sal Moslehian
چکیده

We establish a generalized Hyers–Ulam–Rassias stability theorem in the fuzzy sense. In particular, we introduce the notion of fuzzy approximate Jensen mapping and prove that if a fuzzy approximate Jensen mapping is continuous at a point, then we can approximate it by an everywhere continuous Jensen mapping. As a fuzzy version of a theorem of Schwaiger, we also show that if every fuzzy approximate Jensen type mapping from the natural numbers into a fuzzy normed space can be approximated by an additive mapping, then the fuzzy norm is complete. © 2007 Elsevier B.V. All rights reserved. MSC: Primary, 46S40; Secondary, 39B52; 39B82; 26E50; 46S50

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عنوان ژورنال:
  • Fuzzy Sets and Systems

دوره 159  شماره 

صفحات  -

تاریخ انتشار 2008