Acta Mathematica Vietnamica

, Volume 38, Issue 3, pp 471–485

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

Article

DOI: 10.1007/s40306-013-0028-x

Cite this article as:
Hazarika, B. & Savas, E. Acta Math Vietnam. (2013) 38: 471. doi:10.1007/s40306-013-0028-x

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.

Keywords

Statistical convergenceDouble lacunary sequenceP-convergentn-norm

Mathematics Subject Classification

40A0540B5046A1946A45

Copyright information

© Institute of Mathematics, Vietnam Academy of Science and Technology (VAST) and Springer Science+Business Media Singapore 2013

Authors and Affiliations

  1. 1.Department of MathematicsRajiv Gandhi UniversityDoimukhIndia
  2. 2.Department of MathematicsIstanbul Ticaret UniversityUskudar-IstanbulTurkey