Lacunary I_2-Invariant Convergence and Some Properties

Ulusu, Ugur; Dundar, Erdinc; Nuray, Fatih

doi:10.28924/2291-8639-16-2018-317

Research Article

Lacunary I_2-Invariant Convergence and Some Properties

Ugur Ulusu¹
Erdinc Dundar¹*
Fatih Nuray¹

Afyon Kocatepe University

* Corresponding author

Abstract

In this paper, the concept of lacunary invariant uniform density of any subset $A$ of the set $\mathbb{N}\times\mathbb{N}$ is defined. Associate with this, the concept of lacunary $\mathcal{I}_2$-invariant convergence for double sequences is given. Also, we examine relationships between this new type convergence concept and the concepts of lacunary invariant convergence and $p$-strongly lacunary invariant convergence of double sequences. Finally, introducing lacunary $\mathcal{I}_2^*$-invariant convergence concept and lacunary $\mathcal{I}_2$-invariant Cauchy concepts, we give the relationships among these concepts and relationships with lacunary $\mathcal{I}_2$-invariant convergence concept.

How to Cite

U. Ulusu, E. Dundar, F. Nuray, Lacunary I_2-Invariant Convergence and Some Properties, Int. J. Anal. Appl. 16 (2018), 317–327. https://doi.org/10.28924/2291-8639-16-2018-317

BibTeX

@article{Ulusu2018,
  author  = {Ulusu, Ugur and Dundar, Erdinc and Nuray, Fatih},
  title   = {Lacunary I_2-Invariant Convergence and Some Properties},
  journal = {Int. J. Anal. Appl.},
  volume  = {16},
  year    = {2018},
  pages   = {317--327},
  doi     = {10.28924/2291-8639-16-2018-317}
}

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