Lacunary statistical convergence of double sequences and some inclusion results in n-normed spaces
Acta Mathematica Vietnamica, vol.38, no.3, pp.471-485, 2013 (Scopus)
- Publication Type: Article / Article
- Volume: 38 Issue: 3
- Publication Date: 2013
- Doi Number: 10.1007/s40306-013-0028-x
- Journal Name: Acta Mathematica Vietnamica
- Journal Indexes: Scopus
- Page Numbers: pp.471-485
- Keywords: Statistical convergence, Double lacunary sequence, P-convergent, n-norm
- İstanbul Ticaret University Affiliated: Yes
Abstract
In this paper, we introduce the concept of lacunary statistical convergence of double sequences in n-normed spaces. Some inclusion relations between the sets of statistically convergent and lacunary statistically convergent cases of double sequences are established. In addition, we also define lacunary statistical Cauchy double sequences and prove that this notion is equivalent to the lacunary statistical convergence of double sequences. © 2013 Institute of Mathematics, Vietnam Academy of Science and Technology (VAST) and Springer Science+Business Media Singapore.