## 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.

### MSC:

 39B82 Stability, separation, extension, and related topics for functional equations 28E99 Miscellaneous topics in measure theory 39B52 Functional equations for functions with more general domains and/or ranges 46S10 Functional analysis over fields other than $$\mathbb{R}$$ or $$\mathbb{C}$$ or the quaternions; non-Archimedean functional analysis
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