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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.

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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