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A fixed point approach to the fuzzy stability of an aqcq-functional equation. (English) Zbl 1465.47058

Summary: In [A. K. Mirmostafaee et al., Fuzzy Sets Syst. 159, No. 6, 730–738 (2008; Zbl 1179.46060); A. K. Mirmostafaee and M. S. Moslehian, Fuzzy Sets Syst. 159, No. 6, 720–729 (2008; Zbl 1178.46075)], the fuzzy stability problems for the Cauchy additive functional equation and the Jensen additive functional equation in fuzzy Banach spaces have been investigated.
Using the fixed point method, we prove the Hyers-Ulam stability of the following additive-quadratic-cubic-quartic functional equation \[f(x+2y)+f(x-2y)=4f(x+y)+4f(x-y)-6f(x)+f(2y)+f(-2y)-4f(y)-4f(-y)\] in fuzzy Banach spaces.

MSC:

47S40 Fuzzy operator theory
47H10 Fixed-point theorems
39B52 Functional equations for functions with more general domains and/or ranges
54E40 Special maps on metric spaces
46S40 Fuzzy functional analysis
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