# Hyers-Ulam stability of derivations in fuzzy Banach space

Volume 9, Issue 12, pp 5970--5979
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### Authors

Gang Lu - Department of Mathematics, Zhejiang University, Hangzhou 310027, P. R. China. - Department of Mathematics, School of Science, Shenyang University of Technology, Shenyang 110178, P. R. China. Jun Xie - Department of Mathematics, School of Science, Shenyang University of Technology, Shenyang 110178, P. R. China. Qi Liu - Department of Mathematics, School of Science, Shenyang University of Technology, Shenyang 110178, P. R. China. Yuanfeng Jin - Department of Mathematics, Yanbian University, Yanji 133001, P. R. China.

### Abstract

In this paper, we construct an additive functional equation, and use the fixed point alternative theorem to investigate the Hyers-Ulam stability of derivations fuzzy Banach space and fuzzy Lie Banach space associated with the following functional equation:$f (2x - y - z)+f (x - z)+f (x + y + 2z) = f (4x)$.

### Share and Cite

##### ISRP Style

Gang Lu, Jun Xie, Qi Liu, Yuanfeng Jin, Hyers-Ulam stability of derivations in fuzzy Banach space, Journal of Nonlinear Sciences and Applications, 9 (2016), no. 12, 5970--5979

##### AMA Style

Lu Gang, Xie Jun, Liu Qi, Jin Yuanfeng, Hyers-Ulam stability of derivations in fuzzy Banach space. J. Nonlinear Sci. Appl. (2016); 9(12):5970--5979

##### Chicago/Turabian Style

Lu, Gang, Xie, Jun, Liu, Qi, Jin, Yuanfeng. "Hyers-Ulam stability of derivations in fuzzy Banach space." Journal of Nonlinear Sciences and Applications, 9, no. 12 (2016): 5970--5979

### Keywords

• Fuzzy normed space
• Hyers-Ulam stability
• fixed point alternative
• fuzzy Banach space.

•  39B82
•  46S40
•  39B52
•  46L57

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