On Modulated Lacunary Statistical Convergence of Double Sequences
In earlier works, F. León and coworkers discovered a remarkable structure between statistical convergence and strong Cesàro convergence, modulated by a function <i>f</i> (called a modulus function). Such nice structure pivots around the notion of compatible modulus function. In this pape...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-02-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/11/4/1042 |
| _version_ | 1797619494974128128 |
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| author | María del Pilar Romero de la Rosa |
| author_facet | María del Pilar Romero de la Rosa |
| author_sort | María del Pilar Romero de la Rosa |
| collection | DOAJ |
| description | In earlier works, F. León and coworkers discovered a remarkable structure between statistical convergence and strong Cesàro convergence, modulated by a function <i>f</i> (called a modulus function). Such nice structure pivots around the notion of compatible modulus function. In this paper, we will explore such a structure in the framework of lacunary statistical convergence for double sequences and discover that such structure remains true for <i>lacunary compatible modulus functions</i>. Thus, we continue the work of Hacer Şenül, Mikail Et and Yavuz Altin, and we fully solve some questions posed by them. |
| first_indexed | 2024-03-11T08:28:44Z |
| format | Article |
| id | doaj.art-cde722b99f3b42419fb12f5e922fd5fd |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-11T08:28:44Z |
| publishDate | 2023-02-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-cde722b99f3b42419fb12f5e922fd5fd2023-11-16T21:57:34ZengMDPI AGMathematics2227-73902023-02-01114104210.3390/math11041042On Modulated Lacunary Statistical Convergence of Double SequencesMaría del Pilar Romero de la Rosa0Department of Mathematics, University of Cádiz, Avda. de la Universidad s/n, 11405 Jerez de la Frontera, Cádiz, SpainIn earlier works, F. León and coworkers discovered a remarkable structure between statistical convergence and strong Cesàro convergence, modulated by a function <i>f</i> (called a modulus function). Such nice structure pivots around the notion of compatible modulus function. In this paper, we will explore such a structure in the framework of lacunary statistical convergence for double sequences and discover that such structure remains true for <i>lacunary compatible modulus functions</i>. Thus, we continue the work of Hacer Şenül, Mikail Et and Yavuz Altin, and we fully solve some questions posed by them.https://www.mdpi.com/2227-7390/11/4/1042double sequenceslacunary convergencestatistical convergencestrong Cesàro convergencemodulus function |
| spellingShingle | María del Pilar Romero de la Rosa On Modulated Lacunary Statistical Convergence of Double Sequences Mathematics double sequences lacunary convergence statistical convergence strong Cesàro convergence modulus function |
| title | On Modulated Lacunary Statistical Convergence of Double Sequences |
| title_full | On Modulated Lacunary Statistical Convergence of Double Sequences |
| title_fullStr | On Modulated Lacunary Statistical Convergence of Double Sequences |
| title_full_unstemmed | On Modulated Lacunary Statistical Convergence of Double Sequences |
| title_short | On Modulated Lacunary Statistical Convergence of Double Sequences |
| title_sort | on modulated lacunary statistical convergence of double sequences |
| topic | double sequences lacunary convergence statistical convergence strong Cesàro convergence modulus function |
| url | https://www.mdpi.com/2227-7390/11/4/1042 |
| work_keys_str_mv | AT mariadelpilarromerodelarosa onmodulatedlacunarystatisticalconvergenceofdoublesequences |