On the $\Delta _{{\Lambda ^2}}^f$-Statistical Convergence on Product Time Scale

Bayram Sözbir; Selma Altundağ; Metin Basarır

doi:10.32323/ujma.743949

EN

On the $\Delta _{{\Lambda ^2}}^f$-Statistical Convergence on Product Time Scale

Abstract

In this paper, we first define a new density of a $\Delta $-measurable subset of a product time scale ${\Lambda ^2}$ with respect to an unbounded modulus function. Then, by using this definition, we introduce the concepts of $\Delta _{{\Lambda ^2}}^f$-statistical convergence and $\Delta _{{\Lambda ^2}}^f$-statistical Cauchy for a $\Delta $-measurable real-valued function defined on product time scale ${\Lambda ^2}$ and also obtain some results about these new concepts. Finally, we present the definition of strong $\Delta _{{\Lambda ^2}}^f$-Cesaro summability on ${\Lambda ^2}$ and investigate the connections between these new concepts.

Keywords

Delta measure, Density, Modulus function, Product time scale, Statistical convergence, Strong Cesaro summability

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Details

Primary Language

English

Subjects

Mathematical Sciences

Journal Section

Research Article

Authors

Bayram Sözbir ^*
0000-0002-9475-7180
Türkiye

Selma Altundağ
0000-0002-5893-9868
Türkiye

Metin Basarır
0000-0002-4341-4399
Türkiye

Publication Date

December 23, 2020

Submission Date

May 28, 2020

Acceptance Date

October 22, 2020

Published in Issue

Year 2020 Volume: 3 Number: 4

DOI

https://doi.org/10.32323/ujma.743949

IZ

https://izlik.org/JA77AU23RZ

APA

Sözbir, B., Altundağ, S., & Basarır, M. (2020). On the $\Delta _{{\Lambda ^2}}^f$-Statistical Convergence on Product Time Scale. Universal Journal of Mathematics and Applications, 3(4), 138-143. https://doi.org/10.32323/ujma.743949

AMA

1.Sözbir B, Altundağ S, Basarır M. On the $\Delta _{{\Lambda ^2}}^f$-Statistical Convergence on Product Time Scale. Univ. J. Math. Appl. 2020;3(4):138-143. doi:10.32323/ujma.743949

Chicago

Sözbir, Bayram, Selma Altundağ, and Metin Basarır. 2020. “On the $\Delta _{{\Lambda ^2}}^f$-Statistical Convergence on Product Time Scale”. Universal Journal of Mathematics and Applications 3 (4): 138-43. https://doi.org/10.32323/ujma.743949.

EndNote

Sözbir B, Altundağ S, Basarır M (December 1, 2020) On the $\Delta _{{\Lambda ^2}}^f$-Statistical Convergence on Product Time Scale. Universal Journal of Mathematics and Applications 3 4 138–143.

IEEE

[1]B. Sözbir, S. Altundağ, and M. Basarır, “On the $\Delta _{{\Lambda ^2}}^f$-Statistical Convergence on Product Time Scale”, Univ. J. Math. Appl., vol. 3, no. 4, pp. 138–143, Dec. 2020, doi: 10.32323/ujma.743949.

ISNAD

Sözbir, Bayram - Altundağ, Selma - Basarır, Metin. “On the $\Delta _{{\Lambda ^2}}^f$-Statistical Convergence on Product Time Scale”. Universal Journal of Mathematics and Applications 3/4 (December 1, 2020): 138-143. https://doi.org/10.32323/ujma.743949.

JAMA

1.Sözbir B, Altundağ S, Basarır M. On the $\Delta _{{\Lambda ^2}}^f$-Statistical Convergence on Product Time Scale. Univ. J. Math. Appl. 2020;3:138–143.

MLA

Sözbir, Bayram, et al. “On the $\Delta _{{\Lambda ^2}}^f$-Statistical Convergence on Product Time Scale”. Universal Journal of Mathematics and Applications, vol. 3, no. 4, Dec. 2020, pp. 138-43, doi:10.32323/ujma.743949.

Vancouver

1.Bayram Sözbir, Selma Altundağ, Metin Basarır. On the $\Delta _{{\Lambda ^2}}^f$-Statistical Convergence on Product Time Scale. Univ. J. Math. Appl. 2020 Dec. 1;3(4):138-43. doi:10.32323/ujma.743949