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The stability of the quartic functional equation in various spaces. (English) Zbl 1205.39029
Summary: The purpose of this paper is first to introduce the notation of intuitionistic random normed spaces, and then by virtue of this notation to study the stability of a quartic functional equation in the setting of these spaces under arbitrary triangle norms. Then we prove the stability of above quartic functional equation in non-Archimedean random normed spaces. Furthermore, the interdisciplinary relation among the theory of random spaces, the theory of non-Archimedean spaces, the theory of intuitionistic spaces and the theory of functional equations are also presented in the paper.

39B82Stability, separation, extension, and related topics
28E99Miscellaneous topics of measure theory
39B52Functional equations for functions with more general domains and/or ranges
46S10Functional analysis over fields (not $\Bbb R$, $\Bbb C$, $\Bbb H$or quaternions)
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