Lacunary statistical and lacunary strongly convergence of generalized difference sequences in intuitionistic fuzzy normed linear spaces

Mausumi Sen; Mikail Et

doi:10.5269/bspm.v38i1.34814

Authors

Mausumi Sen National Institute of Technology Silchar Assam Department of Mathematics
Mikail Et Firat University Department of Mathematics

DOI:

https://doi.org/10.5269/bspm.v38i1.34814

Keywords:

Statistical convergence, Lacunary sequence, Intuitionistic fuzzy normed linear space, Difference sequence, Cesaro convergence

Abstract

In this article we introduce the concepts of lacunary statistical convergence and lacunary strongly convergence of generalized difference sequences in intuitionistic fuzzy normed linear spaces and give their characterization. We obtain some inclusion relation relating to these concepts. Further some necessary and sufficient conditions for equality of the sets of statistical convergence and lacunary statistical convergence of generalized difference sequences have been established. The notion of strong Cesaro summability in intuitionistic fuzzy normed linear spaces has been introduced and studied. Also the concept of lacunary generalized difference statistically Cauchy sequence has been introduced and some results are established.