HYERS-ULAM STABILITY OF DERIVATIONS IN FUZZY BANACH SPACE: REVISITED

한국수학교육학회지시리즈B:순수및응용수학 / 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 (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)

Lu, Gang, Jin, Yuanfeng, Wu, Gang, & Yun, Sungsik. (2018). HYERS-ULAM STABILITY OF DERIVATIONS IN FUZZY BANACH SPACE: REVISITED. 한국수학교육학회지시리즈B:순수및응용수학, 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

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Vol.25 No.2

HYERS-ULAM STABILITY OF DERIVATIONS IN FUZZY BANACH SPACE: REVISITED

HYERS-ULAM STABILITY OF DERIVATIONS IN FUZZY BANACH SPACE: REVISITED

Abstract

한국수학교육학회지시리즈B:순수및응용수학