Strong Convergence in Fuzzy Metric Spaces

Abstract

In this paper we introduce and study the concept of strong convergence in fuzzy metric spaces $(X,M,\ast)$ in the sense of George and Veeramani. This concept is related with the condition $\bigwedge_{t>0} M(x,y,t)>0$ which, frequently is required or missing, in this context. Among other results we characterize the class of $s$-fuzzy metrics by the strong convergence defined here and we solve partially the question of finding explicitly a metric \textit{compatible} with a given fuzzy metric.