• Korean Journal of Mathematics
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• 제22권4호
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• pp.659-670
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• 2014

In this paper, we prove the Hyers-Ulam stability of homomorphisms in fuzzy Banach algebras and of derivations on fuzzy Banach algebras associated to the Cauchy-Jensen functional equation.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제25권2호
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• pp.135-147
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• 2018

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.

• 충청수학회지
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• 제23권3호
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• pp.563-570
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• 2010

In this article, we take account of the fuzzy stability for generalized derivation in fuzzy Banach algebra.

• Korean Journal of Mathematics
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• 제20권1호
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• pp.91-106
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• 2012

In this paper, we prove the Hyers-Ulam stability of the Jensen functional equation in fuzzy Banach algebras by using fixed point method and by using direct method.