On statistical convergence in fuzzy metric spaces

The idea of statistical convergence, which was first introduced by Fast and Steinhaus independently in 1951, has become one of the most active area of research in the field of mathematics. Recently, it has been applied to the realm of metrics by several authors and some useful results have been obtained. However, the existence of non-completable fuzzy metric spaces, in the sense of George and Veeramani, demonstrates that the theory of fuzzy metrics seem to be richer than that of metrics. In view of this, we attempt to generalize this convergence to the realm of fuzzy metrics. Firstly, we introduce the concept of sts-convergence in fuzzy metric spaces. Then we characterize those fuzzy metric spaces in which all convergent sequences are sts-convergent. Finally, we study sts-Cauchy sequences in fuzzy metric spaces and sts-completeness of fuzzy metric spaces. © 2020 - IOS Press and the authors. All rights reserved.