On p-statistical convergence in fuzzy metric spaces

Abstract

The idea of statistical convergence was independently presented by Fast and Steinhaus in 1951 and has now become an area of active research in the field of mathematics. Recently, it has been successfully used in the realm of fuzzy metrics, in the sense of George and Veeramani, by several authors. The appearance of a parameter t in the definition of fuzzy metric space allows for the introduction of new particular definitions in fuzzy metric context. In view of this, we introduce the
concept of p-statistical convergence in fuzzy metric spaces and explore some useful results. Also, we give several equivalent characterizations those are relative to the concept of principal fuzzy metric space that Gregori et al. proposed in [12]. Moreover, we provide some illustrative examples.