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Applied Mathematics and Mechanics (English Edition) ›› 2010, Vol. 31 ›› Issue (1): 21-26.doi: https://doi.org/10.1007/s10483-010-0103-6

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Stability of a cubic functional equation in intuitionistic random normed spaces

张石生1 John Michael RASSIAS2  Reza SAADATI3   

  1. 1. Department of Mathematics, Yibin University, Yibin 644007, Sichuan Province, P. R. China;
    2. Section of Mathematics and Informatics, Pedagogical Department, National and Capodistrian University of Athens, Athens 15342, Greece;
    3. Department of Mathematics and Computer Science, Amirkabir University of Technology, Tehran 15914, Iran
  • 收稿日期:2009-07-06 修回日期:2009-11-10 出版日期:2010-01-03 发布日期:2010-01-01

Stability of a cubic functional equation in intuitionistic random normed spaces

ZHANG Shi-Sheng1, John Michael RASSIAS2, Reza SAADATI3   

  1. 1. Department of Mathematics, Yibin University, Yibin 644007, Sichuan Province, P. R. China;
    2. Section of Mathematics and Informatics, Pedagogical Department, National and Capodistrian University of Athens, Athens 15342, Greece;
    3. Department of Mathematics and Computer Science, Amirkabir University of Technology, Tehran 15914, Iran
  • Received:2009-07-06 Revised:2009-11-10 Online:2010-01-03 Published:2010-01-01

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被引次数

31

摘要： 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.

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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