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ISSN : 1226-0657

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Vol.25 No.2
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HYERS-ULAM STABILITY OF DERIVATIONS IN FUZZY BANACH SPACE: REVISITED

Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics / Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, (P)1226-0657; (E)2287-6081
2018, v.25 no.2, pp.135-147
https://doi.org/10.7468/jksmeb.2018.25.2.135
Lu, Gang
Jin, Yuanfeng
Wu, Gang
Yun, Sungsik
Lu,, G. , Jin,, Y. , Wu,, G. , & Yun,, S. (2018). HYERS-ULAM STABILITY OF DERIVATIONS IN FUZZY BANACH SPACE: REVISITED. Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, 25(2), 135-147, https://doi.org/10.7468/jksmeb.2018.25.2.135
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Abstract

Lu et al. [27] defined derivations on fuzzy Banach spaces and fuzzy Lie Banach spaces and proved the Hyers-Ulam stability of derivations on fuzzy Banach spaces and fuzzy Lie Banach spaces. It is easy to show that the definitions of derivations on fuzzy Banach spaces and fuzzy Lie Banach spaces are wrong and so the results of [27] are wrong. Moreover, there are a lot of seroius problems in the statements and the proofs of the results in Sections 2 and 3. In this paper, we correct the definitions of biderivations on fuzzy Banach algebras and fuzzy Lie Banach algebras and the statements of the results in [27], and prove the corrected theorems.

keywords
fuzzy Banach algebra, additive functional equation, Hyers-Ulam stability, fixed point alternative, fuzzy Lie Banach algebra

Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics

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