Hyers-Ulam stability of derivations in fuzzy Banach space

Volume 9, Issue 12, pp 5970--5979 http://dx.doi.org/10.22436/jnsa.009.12.05

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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:\( f (2x - y - z)+f (x - z)+f (x + y + 2z) = f (4x)\).

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Keywords

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

MSC

•  39B82
•  46S40
•  39B52
•  46L57

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