The stability of the quartic functional equation in various spaces

  • Authors:

  • Reza Saadati;Yeol J. Cho;Javad Vahidi

  • Affiliations:

  • Department of Mathematics and Computer Science, Amirkabir University of Technology, 424 Hafez Avenue, Tehran 15914, Iran and Faculty of Sciences, Shomal University, Amol, Iran;Department of Mathematics Education and the RINS, Gyeongsang National University, Chinju 660-701, Republic of Korea;Faculty of Sciences, Shomal University, Amol, Iran

  • Venue:
  • Computers & Mathematics with Applications
  • Year:
  • 2010

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Abstract

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.