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Non-Archimedean \(\mathcal L\)-fuzzy normed spaces and stability of functional equations. (English) Zbl 1205.39023

Summary: J. R. Lee, J. S. An and C. Park [Abstr. Appl. Anal. 2008, Article ID 628178, 8 p. (2008; Zbl 1146.39045)] considered the following quadratic functional equation \(f(lx+y)+f(lx - y)=2l^{2}f(x)+2f(y)\) and proved the Hyers-Ulam-Rassias stability of the above functional equation in classical Banach spaces. In this paper, we prove the Hyers-Ulam-Rassias stability of the above quadratic functional equation in non-Archimedean \(\mathcal L\)-fuzzy normed spaces.

MSC:

39B52 Functional equations for functions with more general domains and/or ranges
39B82 Stability, separation, extension, and related topics for functional equations
46S10 Functional analysis over fields other than \(\mathbb{R}\) or \(\mathbb{C}\) or the quaternions; non-Archimedean functional analysis

Citations:

Zbl 1146.39045
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Full Text: DOI

References:

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