The Pure and Applied Mathematics (한국수학교육학회지시리즈B:순수및응용수학)

Korean Society of Mathematical Education (한국수학교육학회)
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HYERS-ULAM STABILITY OF DERIVATIONS IN FUZZY BANACH SPACE: REVISITED

  • Lu, Gang (Department of Mathematics, Zhejiang University) ;
  • Jin, Yuanfeng (Department of Mathematics, Yanbian University) ;
  • Wu, Gang (Department of Mathematics and Applied Mathematics, Harbin University of Commerce) ;
  • Yun, Sungsik (Department of Financial Mathematics, Hanshin University)
  • Received : 2017.11.28
  • Accepted : 2018.05.04
  • Published : 2018.05.31
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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.

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References

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