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2014 Hyers-Ulam-Rassias Stability of Some Additive Fuzzy Set-Valued Functional Equations with the Fixed Point Alternative
Yonghong Shen, Yaoyao Lan, Wei Chen
Abstr. Appl. Anal. 2014: 1-9 (2014). DOI: 10.1155/2014/139175

Abstract

Let Y be a real separable Banach space and let 𝒦CY,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 𝒦CY,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.

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Yonghong Shen. Yaoyao Lan. Wei Chen. "Hyers-Ulam-Rassias Stability of Some Additive Fuzzy Set-Valued Functional Equations with the Fixed Point Alternative." Abstr. Appl. Anal. 2014 1 - 9, 2014. https://doi.org/10.1155/2014/139175

Information

Published: 2014
First available in Project Euclid: 2 October 2014

zbMATH: 07021791
MathSciNet: MR3178848
Digital Object Identifier: 10.1155/2014/139175

Rights: Copyright © 2014 Hindawi

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