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, issue 1

Abstract: Let Y be a real separable Banach space and let (𝒦C(Y), d∞) be the subspace of all normal fuzzy convex and upper semicontinuous fuzzy sets of Y equipped with the supremum metric d∞. In this paper, we introduce several types of additive fuzzy set‐valued functional equations in (𝒦C(Y), d∞). 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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https://doi.org/10.1155/2014/139175

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:139175

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