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

Abstract

In this paper, we defined the concepts of lacunary $\mathcal{I}^{\ast}$-convergence and strongly lacunary $\mathcal{I}^{\ast}$-convergence. We investigated the relations between strongly lacunary $\mathcal{I}$-convergence and strongly lacunary $\mathcal{I}^{\ast}$-convergence. Also, we defined the concept of strongly lacunary $\mathcal{I}^{\ast}$-Cauchy sequence and investigated the relations between strongly lacunary $\mathcal{I}$-Cauchy sequence and strongly lacunary $\mathcal{I}^{\ast}$-Cauchy sequence.