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

作者：Bhardwaj Vinod K^*; Dhawan Shweta

来源：JOURNAL OF INEQUALITIES AND APPLICATIONS, 2017, 2017(1): 25.

DOI：10.1186/s13660-017-1294-2

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

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 theta for which , where and denote the sets of all f-Wijsman lacunary statistically convergent sequences and f-Wijsman statistically convergent sequences, respectively.

• 出版日期2017-1-23