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2023•Communications in Advanced Mathematical SciencesOpen access

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

Nimet PANCAROĞLU AKIN, Erdınç Dündar

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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.

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What this paper is about

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.

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Available 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.

Key concepts: Lacunary function, Mathematics, Sequence (biology), Convergence (economics), Cauchy distribution, Cauchy sequence, Combinatorics, Pure mathematics

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