Stability of derivations in fuzzy normed algebras
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1989
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Authors
Yeol Je Cho
- Department of Mathematics Education and the RINS, Gyeongsang National University, Chinju 660-701, Korea.
Choonkill Park
- Research Institute for Natural Sciences, Hanyang University, Seoul 133-791, Korea.
Young-Oh Yang
- Department of Mathematics, Jeju National University, Jeju 690-756, Korea.
Abstract
In this paper, we find a fuzzy approximation of derivation for an m-variable additive functional equation. In
fact, using the fixed point method, we prove the Hyers-Ulam stability of derivations on fuzzy Lie \(C^*\)-algebras
for the the following additive functional equation
\[\Sigma^m _{i=1} f ( mx_i + \Sigma^m _{j=1, j\neq i} x_j ) + f (\Sigma^m _{i=1} x_i ) = 2f (\Sigma^m_{ i=1} mx_i )\]
for a given integer m with \(m \geq 2\).
Share and Cite
ISRP Style
Yeol Je Cho, Choonkill Park, Young-Oh Yang, Stability of derivations in fuzzy normed algebras, Journal of Nonlinear Sciences and Applications, 8 (2015), no. 1, 1--7
AMA Style
Cho Yeol Je, Park Choonkill, Yang Young-Oh, Stability of derivations in fuzzy normed algebras. J. Nonlinear Sci. Appl. (2015); 8(1):1--7
Chicago/Turabian Style
Cho, Yeol Je, Park, Choonkill, Yang, Young-Oh. "Stability of derivations in fuzzy normed algebras." Journal of Nonlinear Sciences and Applications, 8, no. 1 (2015): 1--7
Keywords
- Fuzzy normed space
- additive functional equation
- fixed point
- derivation
- \(C^*\)-algebra
- Lie \(C^*\)-algebra
- Hyers-Ulam stability.
MSC
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