Intuitionistic fuzzy stability of a Jensen functional equation via fixed point technique

The object of this paper is to determine Hyers-Ulam-Rassias stability concerning the Jensen functional equation in intuitionistic fuzzy normed space (IFNS) by using the fixed point method. Further, we establish stability of the Cauchy functional equation in IFNS.

[1]  Q. M. Danish Lohani,et al.  On generalized statistical convergence in intuitionistic fuzzy normed space , 2009 .

[2]  Viorel Radu,et al.  THE FIXED POINT ALTERNATIVE AND THE STABILITY OF FUNCTIONAL EQUATIONS , 2003 .

[3]  J. C. Parnami,et al.  On Jensen's functional equation , 1992 .

[4]  Mohammad Mursaleen,et al.  Nonlinear operators between intuitionistic fuzzy normed spaces and Fréchet derivative , 2009 .

[5]  R. Saadati.  On the intuitionistic fuzzy topological spaces , 2005, math/0501149.

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

[7]  Mohammad Mursaleen,et al.  On the ideal convergence of double sequences in intuitionistic fuzzy normed spaces , 2010, Comput. Math. Appl..

[8]  Soon‐Yeong Chung,et al.  Stability of a Jensen type functional equation , 2007 .

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

[10]  S. A. Mohiuddine.  Stability of Jensen functional equation in intuitionistic fuzzy normed space , 2009 .

[11]  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.

[12]  Mohammad Mursaleen,et al.  On lacunary statistical convergence with respect to the intuitionistic fuzzy normed space , 2009, J. Comput. Appl. Math..

[13]  S. A. Mohiuddine,et al.  On stability of a cubic functional equation in intuitionistic fuzzy normed spaces , 2009 .

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

[15]  Zygíryd Kominek,et al.  On a Local Stability of the Jensen Functional Equation , 1989 .

[16]  Dorel Mihet,et al.  The fixed point method for fuzzy stability of the Jensen functional equation , 2009, Fuzzy Sets Syst..

[17]  Syed Abdul Mohiuddine,et al.  Stability of Pexiderized quadratic functional equation in intuitionistic fuzzy normed space , 2011, J. Comput. Appl. Math..

[18]  J. B. Díaz,et al.  A fixed point theorem of the alternative, for contractions on a generalized complete metric space , 1968 .

[19]  Soon-Mo Jung,et al.  Hyers-Ulam-Rassias stability of Jensen's equation and its application , 1998 .

[20]  Alireza Kamel Mirmostafaee,et al.  Fuzzy versions of Hyers-Ulam-Rassias theorem , 2008, Fuzzy Sets Syst..