On statistical convergence of sequences of closed sets in metric spaces

Abstract

Abstract In this paper, we do further investigations on the statistical inner and outer limits of sequences of closed sets in metric spaces, which were introduced by Nuray, Rhoades, and Talo, Sever, Başar, and generalize the conventional Painleve-Kuratowski inner and outer limits. Also, we provide criteria for checking statistical Wijsman and Hausdorff set convergences and we examine the relationship between Kuratowski and Wijsman statistical convergence. A closer look on the concept of statistical Cauchyness, with respect to the Hausdorff “extended” metric h, completes this research.