Hyers-Ulam-Rassias stability of some additive fuzzy set-valued functional equations with the fixed point alternative (Q1722161)

Summary: Let \(Y\) be a real separable Banach space and let \(\left(\mathcal{K}_C \left(Y\right), d_\infty\right)\) be the subspace of all normal fuzzy convex and upper semicontinuous fuzzy sets of \(Y\) equipped with the supremum metric \(d_\infty\). In this paper, we introduce several types of additive fuzzy set-valued functional equations in \(\left(\mathcal{K}_C \left(Y\right), d_\infty\right)\). 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.