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J Inequal Appl. 2017;2017(1):25. doi: 10.1186/s13660-017-1294-2. Epub 2017 Jan 23.

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

Author information

1
Department of Mathematics, Kurukshetra University, Kurukshetra, 136119 India.
2
Department of Mathematics, KVA DAV College for Women, Karnal, 132001 India.

Abstract

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

KEYWORDS:

Wijsman convergence; density; lacunary sequence; lacunary strong convergence; modulus function; statistical convergence

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