Title: On Lacunary $\mathcal{I}_2^{\ast }$-Convergence and Lacunary $\mathcal{I}_2^{\ast }$-Cauchy Sequence
Abstract: In the study conducted here, we gave some newly concepts in summability. In this sense, firstly, we gave the concept of lacunary $\mathcal{I}_2^{\ast}$-convergence and we investigate the relations between lacunary $\mathcal{I}_2$-convergence and lacunary $\mathcal{I}_2^{\ast}$-convergence. Also, we gave the concept of lacunary $\mathcal{I}_2^{\ast}$-Cauchy sequence and investigate the relations between lacunary $\mathcal{I}_2$-Cauchy sequence and lacunary $\mathcal{I}_2^{\ast}$-Cauchy sequence.