New Convergence Definitions for Sequences of Sets

Abstract

Several notions of convergence for subsets of metric space appear in the literature. In this paper, we define Wijsman $I$-convergence and Wijsman $I^{*}$-convergence for sequences of sets and establish some basic theorems. Furthermore, we introduce the concepts of Wijsman I-Cauchy sequence and Wijsman $I^{*}$-Cauchy sequence and then study their certain properties.