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 off-Wijsman lacunary statistical convergence of sequences of sets, wherefis 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 modulusf, the concepts of Wijsman lacunary strong convergence with respect to a modulusfandf-Wijsman lacunary statistical convergence are equivalent on bounded sequences. We further characterize thoseθfor which [Formula: see text], where [Formula: see text] and [Formula: see text] denote the sets of allf-Wijsman lacunary statistically convergent sequences andf-Wijsman statistically convergent sequences, respectively.
Department of Mathematics, Kurukshetra University, Kurukshetra, 136119 India.
Vinod K
VK
Bhardwaj
Department of Mathematics, KVA DAV College for Women, Karnal, 132001 India.
Shweta
S
Dhawan
Wijsman convergence; density; lacunary sequence; lacunary strong convergence; modulus function; statistical convergence