On Lacunary $\mathcal{I}_2^{\ast }$-Convergence and Lacunary $\mathcal{I}_2^{\ast }$-Cauchy Sequence

Abstract

In the study conducted here, we have given some new concepts in summability. In this sense, firstly, we have given the concept of lacunary $\mathcal{I}_2^{\ast}$-convergence and we have investigated the relations between lacunary $\mathcal{I}_2$-convergence and lacunary $\mathcal{I}_2^{\ast}$-convergence. Also, we have given the concept of lacunary $\mathcal{I}_2^{\ast}$-Cauchy sequence and investigated the relations between lacunary $\mathcal{I}_2$-Cauchy sequence and lacunary $\mathcal{I}_2^{\ast}$-Cauchy sequence.

Keywords

• double sequence
• ideal convergence
• ideal cauchy sequence
• lacunary sequence