Notes to the paper “Fixed points in intuitionistic fuzzy metric spaces” and its generalization to L-fuzzy metric spaces

Recently, Alaca et al. [Alaca et al., Chaos, Solitons & Fractals 2006;29:1073-9] proved some fixed point theorems in intuitionistic fuzzy metric spaces by a strong definition of Cauchy sequence (see [George and Veeramani, Fuzzy Sets Syst 1994;64:395-9] and [Veeramani and Vasuki, Fuzzy Sets Syst 2003;135:409-13]), also the intuitionistic fuzzy metric space has extra conditions (see [Gregori et al., Chaos, Solitons & Fractals, 2006;28:902-5]). In this paper, we consider generalized intuitionistic fuzzy metric spaces i.e., L-fuzzy metric spaces and prove the fuzzy version of Banach and Edelstein contraction theorems in these spaces for modified definition of Cauchy sequence.