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

Abstract

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