Hyers-Ulam-Rassias Stability of Some Additive Fuzzy Set-Valued Functional Equations with the Fixed Point Alternative

Yonghong Shen, Yaoyao Lan and Wei Chen

Abstract and Applied Analysis, 2014, vol. 2014, 1-9

Abstract:

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.

Date: 2014
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:139175

DOI: 10.1155/2014/139175

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