Stability of Jensen functional equation in intuitionistic fuzzy normed space q S.A. Mohiuddine Department of Mathematics, Aligarh Muslim University, Aligarh 202002, India article info Article history: Accepted 3 April 2009 abstract In this paper, we determine some stability results concerning the Jensen functional equa- tion 2f ððx þ yÞ=2Þ¼ f ðxÞþ f ðyÞ in intuitionistic fuzzy normed spaces (IFNS). We define the intuitionistic fuzzy continuity of the Jensen mappings and prove that the existence of a solution for any approximately Jensen mapping implies the completeness of IFNS. Ó 2009 Elsevier Ltd. All rights reserved. 1. Introduction and preliminaries Fuzzy set theory is a powerful hand set for modelling uncertainty and vagueness in various problems arising in the field of science and engineering. It has also very useful applications in various fields, e.g., population dynamics [2], chaos control [10], computer programming [11], nonlinear dynamical systems [12], nonlinear operators [23], statistical convergence [21,22], stability problem [24], etc. The fuzzy topology proves to be a very useful tool to deal with such situations where the use of classical theories breaks down. The most fascinating application of fuzzy topology in quantum particle physics arises in string and  ð1Þ -theory of El-Naschie (cf. [3–9,17,18]) who presented the relation of fuzzy Kähler interpolation of  ð1Þ to the recent work on cosmo-topology and the Poincaré dodecahedral conjecture and gave various applications and re- sults of  ð1Þ -theory from nano technology to brain research. There are many situations where the norm of a vector is not possible to find and the concept of intuitionistic fuzzy norm [25,29] seems to be more suitable in such cases, that is, we can deal with such situations by modelling the inexactness through the intuitionistic fuzzy norm. Stability problem of a functional equation was first posed by Ulam [30] which was answered by Hyers [13] and then gen- eralized by Aoki [1] and Rassias [27] for additive mappings and linear mappings, respectively. Since then several stability problems for various functional equations have been investigated in [14] and [28]; and various fuzzy stability results con- cerning Jensen functional equations were discussed in [15,16,19] and [20]. In this paper, we determine some stability results concerning the Jensen functional equation 2f ððx þ yÞ=2Þ¼ f ðxÞþ f ðyÞ in intuitionistic fuzzy normed spaces. We define the intuitionistic fuzzy continuity of the Jensen mappings and prove that the existence of a solution for any approximately Jensen mapping implies the completeness of intuitionistic fuzzy normed spaces (IFNS). In this section, we recall some notations and basic definitions used in this paper. Definition 1.1. A binary operation  : ½0; 1½0; 1!½0; 1 is said to be a continuous t-norm if it satisfies the following conditions: 0960-0779/$ - see front matter Ó 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.chaos.2009.04.040 q The present research is supported by the Department of Atomic Energy, Government of India under the NBHM-Post Doctoral Fellowship programme number 40/10/2008-R&D II/892. E-mail address: mohiuddine@gmail.com Chaos, Solitons and Fractals 42 (2009) 2989–2996 Contents lists available at ScienceDirect Chaos, Solitons and Fractals journal homepage: www.elsevier.com/locate/chaos