Iλ-convergence in intuitionistic fuzzy n-normed linear space

The notion of lacunary ideal convergence in intuitionistic fuzzy normed linear space (IFNLS) was introduced by the present corresponding author [P. Debnath, Lacunary ideal convergence in intuitionistic fuzzy normed linear spaces, Comput. Math. Appl., 63 (2012), 708-715] and an open problem in that paper was whether every lacunary I-convergent sequence is lacunary I-Cauchy. Further, a new concept of convergence of sequences in an intuitionistic fuzzy n-normed linear space (IFnNLS) was given in [M. Sen, P. Debnath, Lacunary statistical convergence in intuitionistic fuzzy n-normed linear spaces, Math. Comput. Modelling, 54 (2011), 2978-2985]. With the help of this new definition of convergence, the main aim of this paper is to introduce the concept of Iλ-convergence in an IFnNLS, where I is an ideal of a family of subsets of positive integers N. We also define Iλ-limit points and Iλ-cluster points and establish relations between them. Finally we introduce the notion of Iλ-Cauchy sequence in IFnNLS. We improve and extend some existing results and give a positive answer to the open problem mentioned above in the setting of an IFnNLS. 2010 AMS Classification: 46H25, 46H25, 46A99, 60H10