an:06413643
Zbl 1310.39021
Shen, Yonghong; Chen, Wei; Lan, Yaoyao
On the Ulam type stability of several types of quadratic fuzzy set-valued functional equations
EN
J. Inequal. Appl. 2015, Paper No. 6, 19 p. (2015).
00342272
2015
j
39B82 39B52 46S40
Ulam-type stability; Hausdorff separation; supremum metric; quadratic fuzzy set-valued functional equation; Banach space; Hyers-Ulam stability; direct method
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.