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

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  • Yonghong Shen
  • Yaoyao Lan
  • Wei Chen

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.

Suggested Citation

  • Yonghong Shen & Yaoyao Lan & Wei Chen, 2014. "Hyers-Ulam-Rassias Stability of Some Additive Fuzzy Set-Valued Functional Equations with the Fixed Point Alternative," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-9, March.
    • Handle: RePEc:hin:jnlaaa:139175
    DOI: 10.1155/2014/139175
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