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Zbl 1205.39029
Saadati, Reza; Cho, Yeol J.; Vahidi, Javad
The stability of the quartic functional equation in various spaces. (English)
[J] Comput. Math. Appl. 60, No. 7, 1994-2002 (2010). ISSN 0898-1221

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 2000:: *39B82 Stability, separation, extension, and related topics
28E99 Miscellaneous topics of measure theory
39B52 Functional equations for functions with more general domains
46S10 Functional analysis over fields (not R, C, or quaternions)

Keywords: stability; quartic functional equation; intuitionistic random normed space; non-archimedean random normed spaces

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