Lacunary statistical convergence of double sequences and some inclusion results in n-normed spaces

Hazarika B., Savas E.

Acta Mathematica Vietnamica, vol.38, no.3, pp.471-485, 2013 (Scopus) identifier

  • 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: Double lacunary sequence, n-norm, P-convergent, Statistical convergence
  • Uşak University Affiliated: No

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.