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Hyers-Ulam-Rassias stability of some additive fuzzy set-valued functional equations with the fixed point alternative. (English) Zbl 07021791
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.

##### MSC:
 26 Real functions 54 General topology
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