Lacunary statistical summability of sequences of sets

Abstract

In this paper we define the WS_θ-analog of the Cauchy criterion for convergence and show that it is equivalent to Wijsman lacunary statistical convergence. Also, Wijsman lacunary statistical convergence is compared to other summability methods which are defined in this paper. After giving new definitions for convergence, we prove a result comparing them. In addition, we give the relationship between Wijsman lacunary statistical convergence and Hausdorf lacunary statistical convergence