Density by moduli and Wijsman lacunary statistical convergence of sequences of sets.

The main object of this paper is to introduce and study a new concept of -Wijsman lacunary statistical convergence of sequences of sets, where is an unbounded modulus. The definition of Wijsman lacunary strong convergence of sequences of sets is extended to a definition of Wijsman lacunary strong convergence with respect to a modulus for sequences of sets and it is shown that, under certain conditions on a modulus , the concepts of Wijsman lacunary strong convergence with respect to a modulus and -Wijsman lacunary statistical convergence are equivalent on bounded sequences. We further characterize those for which [Formula: see text], where [Formula: see text] and [Formula: see text] denote the sets of all -Wijsman lacunary statistically convergent sequences and -Wijsman statistically convergent sequences, respectively.