- Universal Journal of Mathematics and Applications
- Cilt: 6 Sayı: 4
- On Strongly Lacunary $\\mathcal{I}_2^{\\ast }$-Convergence and Strongly Lacunary $\\mathcal{I}_2^{\\...
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 : 69 | Download : 114
Publication Date : 2023-12-18
Article Type : Research
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