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On the Ulam type stability of several types of quadratic fuzzy set-valued functional equations. (English) Zbl 1310.39021
Summary: Let \(Y\) be a real separable Banach space and \((\mathcal {F}_{KC}(Y),d_{\infty})\) be the space of all normal fuzzy convex and upper semicontinuous fuzzy sets with compact support in \(Y\), where \(d_{\infty}\) stands for the supremum metric in \(\mathcal{F}_{KC}(Y)\). In the present paper, several types of quadratic fuzzy set-valued functional equations are introduced based on the space mentioned above. We prove the Hyers-Ulam stability of the standard quadratic fuzzy set-valued functional equation by using the fixed point technique. Simultaneously, we also establish some Ulam type stability results of the Deeba and Appolonius type fuzzy set-valued functional equations by employing the direct method, respectively. The stability results of the corresponding single-valued and set-valued functional equations acting as special cases will be included in our results.
MSC:
39B82 Stability, separation, extension, and related topics for functional equations
39B52 Functional equations for functions with more general domains and/or ranges
46S40 Fuzzy functional analysis
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