Stability of a cubic functional equation in intuitionistic random normed spaces

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.

[1]  D. H. Hyers.  On the Stability of the Linear Functional Equation. , 1941, Proceedings of the National Academy of Sciences of the United States of America.

[2]  Themistocles M. Rassias,et al.  On the Stability of Functional Equations and a Problem of Ulam , 2000 .

[3]  R. Saadati,et al.  The stability of an additive functional equation in menger probabilistic φ-normed spaces , 2011 .

[4]  T. Rassias.  On the stability of the linear mapping in Banach spaces , 1978 .

[5]  S. Czerwik,et al.  Functional equations and inequalities in several variables , 2002 .

[6]  Tosio Aoki,et al.  On the Stability of the linear Transformation in Banach Spaces. , 1950 .

[7]  Reza Saadati,et al.  On the Stability of Cubic Mappings and Quadratic Mappings in Random Normed Spaces , 2008 .

[8]  Alireza Kamel Mirmostafaee,et al.  Fuzzy stability of the Jensen functional equation , 2008, Fuzzy Sets Syst..

[9]  Taekyun Kim,et al.  A Note on the -Euler Measures , 2009 .

[10]  S. Ulam.  Problems in modern mathematics , 1964 .

[11]  S. M. Vaezpour,et al.  The Stability of the Quartic Functional Equation in Random Normed Spaces , 2010 .

[12]  Krassimir T. Atanassov,et al.  Intuitionistic fuzzy sets , 1986 .

[13]  M. Moslehian,et al.  On the stability of J*-homomorphisms , 2005, math/0501158.

[14]  M. Moslehian,et al.  A fixed point approach to stability of a quadratic equation , 2005, math/0512007.

[15]  K. Jun,et al.  The generalized Hyers–Ulam–Rassias stability of a cubic functional equation☆ , 2002 .

[16]  Themistocles M. Rassias,et al.  Functional equations, inequalities and applications , 2003 .

[17]  Etienne E. Kerre,et al.  On the relationship between some extensions of fuzzy set theory , 2003, Fuzzy Sets Syst..

[18]  George Isac,et al.  Stability of Functional Equations in Several Variables , 1998 .

[19]  Claudi Alsina,et al.  On the Stability of a Functional Equation Arising in Probabilistic Normed Spaces , 1985 .

[20]  Berthold Schweizer,et al.  Probabilistic Metric Spaces , 2011 .

[21]  Adnan Tuna,et al.  Generalized contraction mapping principle in intuitionistic Menger spaces and application to differential equations , 2007 .

[22]  J. Tabor,et al.  Generalized Pexider equation on a restricted domain , 2008 .

[23]  Viorel Radu,et al.  On the stability of the additive Cauchy functional equation in random normed spaces , 2008, Appl. Math. Lett..