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

Authors : Nimet Pancaroğlu Akin, Erdinç Dündar

Pages : 188-195

Doi:10.33434/cams.1363596

View : 87 | Download : 93

Publication Date : 2023-12-25

Article Type : Research Paper

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