Density by moduli and Wijsman lacunary statistical convergence of sequences of sets
Copyright policy )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 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.
- Kurukshetra University India
- DAV College, Chandigarh India
density, Wijsman convergence, Applied Mathematics, Research, modulus function, lacunary strong convergence, Convergence in general topology (sequences, filters, limits, convergence spaces, nets, etc.), lacunary sequence, Summability in abstract structures, Ideal and statistical convergence, QA1-939, Summability methods using statistical convergence, Discrete Mathematics and Combinatorics, statistical convergence, Mathematics, Analysis
density, Wijsman convergence, Applied Mathematics, Research, modulus function, lacunary strong convergence, Convergence in general topology (sequences, filters, limits, convergence spaces, nets, etc.), lacunary sequence, Summability in abstract structures, Ideal and statistical convergence, QA1-939, Summability methods using statistical convergence, Discrete Mathematics and Combinatorics, statistical convergence, Mathematics, Analysis
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