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

Authors : Erdinç Dündar, Nimet Pancaroğlu Akin, Esra Gülle

Pages : 155-161

Doi:10.32323/ujma.1376849

View : 74 | Download : 125

Publication Date : 2023-12-18

Article Type : Research Paper

Abstract :In the study conducted here, we have given some new concepts in summability theory. In this sense, firstly, using the lacunary sequence we have given the concept of strongly $\\mathcal{I}_{\\theta_2}^{\\ast}$-convergence and we have examined the relations between $\\mathcal{I}_{\\theta_2}^{\\ast}$-convergence and strongly $\\mathcal{I}_{\\theta_2}^{\\ast}$-convergence and also between strongly $\\mathcal{I}_{\\theta_2}$-convergence and strongly $\\mathcal{I}_{\\theta_2}^{\\ast}$-convergence. Also, using the lacunary sequence we have given the concept of strongly $\\mathcal{I}_{\\theta_2}^{\\ast}$-Cauchy sequence and examined the relations between strongly $\\mathcal{I}_{\\theta_2}$-Cauchy sequence and strongly $\\mathcal{I}_{\\theta_2}^{\\ast}$-Cauchy sequence.
Keywords : \\mathcal I 2 Cauchy Sequence, \\mathcal I 2 Convergence, Double sequence, Ideal, Lacunary sequence