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Stability of a cubic functional equation in intuitionistic random normed spaces

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Abstract

In this paper, the stability of a cubic functional equation in the setting of intuitionistic random normed spaces is proved. We first introduce the notation of intuitionistic random normed spaces. Then, by virtue of this notation, we study the stability of a cubic functional equation in the setting of these spaces under arbitrary triangle norms. Furthermore, we present the interdisciplinary relation among the theory of random spaces, the theory of intuitionistic spaces, and the theory of functional equations.

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Authors and Affiliations

  1. Department of Mathematics, Yibin University, Yibin, 644007, Sichuan Province, P. R. China

    Shi-sheng Zhang  (张石生)

  2. Section of Mathematics and Informatics, Pedagogical Department, National and Capodistrian University of Athens, Athens, 15342, Greece

    John Michael Rassias

  3. Department of Mathematics and Computer Science, Amirkabir University of Technology, Tehran, 15914, Iran

    Reza Saadati

Authors
  1. Shi-sheng Zhang  (张石生)
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  2. John Michael Rassias
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  3. Reza Saadati
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Corresponding author

Correspondence to Reza Saadati.

Additional information

Contributed by Shi-sheng ZHANG

Project supported by the Natural Science Foundation of Yibin University (No. 2009Z003)

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Zhang, Ss., Rassias, J.M. & Saadati, R. Stability of a cubic functional equation in intuitionistic random normed spaces. Appl. Math. Mech.-Engl. Ed. 31, 21–26 (2010). https://doi.org/10.1007/s10483-010-0103-6

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  • DOI: https://doi.org/10.1007/s10483-010-0103-6

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