On the $\Delta _{{\Lambda ^2}}^f$-Statistical Convergence on Product Time Scale
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...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Emrah Evren KARA
2020-12-01
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| Series: | Universal Journal of Mathematics and Applications |
| Subjects: | |
| Online Access: | https://dergipark.org.tr/tr/download/article-file/1123126 |
| _version_ | 1797350231888625664 |
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| author | Metin Basarır Bayram Sözbir Selma Altundağ |
| author_facet | Metin Basarır Bayram Sözbir Selma Altundağ |
| author_sort | Metin Basarır |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-08T12:41:43Z |
| format | Article |
| id | doaj.art-c98bfe22ef04403e96c8bb9834a2e46d |
| institution | Directory Open Access Journal |
| issn | 2619-9653 |
| language | English |
| last_indexed | 2024-03-08T12:41:43Z |
| publishDate | 2020-12-01 |
| publisher | Emrah Evren KARA |
| record_format | Article |
| series | Universal Journal of Mathematics and Applications |
| spelling | doaj.art-c98bfe22ef04403e96c8bb9834a2e46d2024-01-21T10:03:06ZengEmrah Evren KARAUniversal Journal of Mathematics and Applications2619-96532020-12-013413814310.32323/ujma.7439491225On the $\Delta _{{\Lambda ^2}}^f$-Statistical Convergence on Product Time ScaleMetin Basarır0Bayram Sözbir1Selma Altundağ2SAKARYA UNIVERSITYSAKARYA UNIVERSITYSAKARYA UNIVERSITYIn 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.https://dergipark.org.tr/tr/download/article-file/1123126delta measuredensitymodulus functionproduct time scalestatistical convergencestrong cesaro summability |
| spellingShingle | Metin Basarır Bayram Sözbir Selma Altundağ On the $\Delta _{{\Lambda ^2}}^f$-Statistical Convergence on Product Time Scale Universal Journal of Mathematics and Applications delta measure density modulus function product time scale statistical convergence strong cesaro summability |
| title | On the $\Delta _{{\Lambda ^2}}^f$-Statistical Convergence on Product Time Scale |
| title_full | On the $\Delta _{{\Lambda ^2}}^f$-Statistical Convergence on Product Time Scale |
| title_fullStr | On the $\Delta _{{\Lambda ^2}}^f$-Statistical Convergence on Product Time Scale |
| title_full_unstemmed | On the $\Delta _{{\Lambda ^2}}^f$-Statistical Convergence on Product Time Scale |
| title_short | On the $\Delta _{{\Lambda ^2}}^f$-Statistical Convergence on Product Time Scale |
| title_sort | on the delta lambda 2 f statistical convergence on product time scale |
| topic | delta measure density modulus function product time scale statistical convergence strong cesaro summability |
| url | https://dergipark.org.tr/tr/download/article-file/1123126 |
| work_keys_str_mv | AT metinbasarır onthedeltalambda2fstatisticalconvergenceonproducttimescale AT bayramsozbir onthedeltalambda2fstatisticalconvergenceonproducttimescale AT selmaaltundag onthedeltalambda2fstatisticalconvergenceonproducttimescale |