The stability of the quartic functional equation in various spaces

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...

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Bibliographic Details
Published in:Computers & mathematics with applications (1987) 2010-10, Vol.60 (7), p.1994-2002
Main Authors: Saadati, Reza, Cho, Yeol J., Vahidi, Javad
Format: Article
Language:English
Subjects:
Intuitionistic random normed space
Mathematical analysis
Mathematical models
Non-Archimedean random normed spaces
Norms
Quartic functional equation
Stability
Triangles
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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.
ISSN:0898-1221
1873-7668
DOI:10.1016/j.camwa.2010.07.034