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

中文翻译：

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双序列的规则理想不变收敛

在本文中，我们介绍了规则不变收敛、规则强不变收敛、规则p-强不变收敛、规则$(\mathcal{I}_{\sigma },\mathcal{I}^{\sigma }_ {2})$ -收敛，规则 $(\mathcal{I}_{\sigma }^{*},\mathcal{I}^{\sigma *}_{2})$ -收敛，规则 $(\ mathcal{I}_{\sigma },\mathcal{I}^{\sigma }_{2} )$ -Cauchy 双序列，规则 $(\mathcal{I}_{\sigma }^{*},\ mathcal{I}^{\sigma *}_{2})$ -Cauchy 双序列并研究它们之间的关系。