Regularly ideal invariant convergence of double sequences

Abstract

Abstract In this paper, we introduce the notions of regularly invariant convergence, regularly strongly invariant convergence, regularly p-strongly invariant convergence, regularly ( I σ , I 2 σ ) $(\mathcal{I}_{\sigma },\mathcal{I}^{\sigma }_{2})$ -convergence, regularly ( I σ ∗ , I 2 σ ∗ ) $(\mathcal{I}_{\sigma }^{*},\mathcal{I}^{\sigma *}_{2})$ -convergence, regularly ( I σ , I 2 σ ) $(\mathcal{I}_{\sigma },\mathcal{I}^{\sigma }_{2} )$ -Cauchy double sequence, regularly ( I σ ∗ , I 2 σ ∗ ) $(\mathcal{I}_{\sigma }^{*},\mathcal{I}^{\sigma *}_{2})$ -Cauchy double sequence and investigate the relationship among them.

Keywords

• Regularly ideal convergence
• Regularly ideal Cauchy sequence
• Invariant convergence
• Double sequence