Abstract
Abstract Recently, Abbas et al. (Fixed Point Theory Appl. 2012:187, 2012) proved tripled fixed point and tripled coincidence point theorems in intuitionistic fuzzy normed spaces. Saadati and Park proved that the topology τ ( μ , ν ) generated by an intuitionistic fuzzy normed space ( X , μ , ν , ∗ , ⋄ ) coincides with the topology τ μ generated by the generalized fuzzy normed space ( X , μ , ∗ ) , and thus the results obtained in intuitionistic fuzzy normed spaces are immediate consequences of the corresponding results for fuzzy normed spaces. In this paper, we improve and extend the results presented by Abbas et al. to ℒ-fuzzy normed spaces. MSC: 47H09, 47H10, 54H25.
Highlights
1 Introduction Intuitionistic fuzzy normed spaces were investigated by Saadati and Park [ ]. They introduced and studied intuitionistic fuzzy normed spaces based both on the idea of intuitionistic fuzzy sets due to Atanassov [ ] and the concept of fuzzy normed spaces given by Saadati and Vaezpour in [ ]
In [ ] Saadati and Park proved that the topology τ(μ,ν) generated by an intuitionistic fuzzy normed space (X, μ, ν, ∗, ) coincides with the topology τμ generated by the generalized fuzzy normed space (X, μ, ∗), and the results obtained in intuitionistic fuzzy normed spaces are immediate consequences of the corresponding results for fuzzy normed spaces
One of the most interesting research topics in fuzzy topology is to find an appropriate definition of fuzzy metric space for its possible applications in several areas
Summary
Intuitionistic fuzzy normed spaces were investigated by Saadati and Park [ ]. There exists considerable literature about fixed point properties for mappings defined on fuzzy metric spaces, which have been studied by many authors (see [ – ]).
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