Let Y be a real separable Banach space and let be the subspace of all normal fuzzy convex and upper semicontinuous fuzzy sets of Y equipped with the supremum metric . In this paper, we introduce several types of additive fuzzy set-valued functional equations in . Using the fixed point technique, we discuss the Hyers-Ulam-Rassias stability of three types additive fuzzy set-valued functional equations, that is, the generalized Cauchy type, the Jensen type, and the Cauchy-Jensen type additive fuzzy set-valued functional equations. Our results can be regarded as important extensions of stability results corresponding to single-valued functional equations and set-valued functional equations, respectively.
"Hyers-Ulam-Rassias Stability of Some Additive Fuzzy Set-Valued Functional Equations with the Fixed Point Alternative." Abstr. Appl. Anal. 2014 1 - 9, 2014. https://doi.org/10.1155/2014/139175