Study of Statistical Convergence of Triple Sequences in a Topological Space
In this paper, we introduce statistical convergence of triple sequences which are defined in a topological space. Various results on statistically convergent triple sequences are produced by using the notion of triple natural density operator. Moreover, we initiate the concept of -convergence of tri...
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| Language: | English |
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Corporación Universitaria Republicana
2025-01-01
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| Series: | Revista Ingeniería, Matemáticas y Ciencias de la Información |
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| Online Access: | https://ojs.urepublicana.edu.co/index.php/ingenieria/article/view/1135 |
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| author | Birojit Das Apurba Debnath Carlos Granados Abdullah Aydin |
| author_facet | Birojit Das Apurba Debnath Carlos Granados Abdullah Aydin |
| author_sort | Birojit Das |
| collection | DOAJ |
| description | In this paper, we introduce statistical convergence of triple sequences which are defined in a topological space. Various results on statistically convergent triple sequences are produced by using the notion of triple natural density operator. Moreover, we initiate the concept of -convergence of triple sequence and establish the interrelationship among -convergence and -converegnce. We see that the first one implies the second one but it’s not vice-versa. But if we restrict the triple sequences to hold the property of first countability, we verify that these notions becomes equivalent. Finally, we prove that the family of all statistically convergent triple sequences under some conditions generates a topological structure within the topological space where they have been defined. |
| format | Article |
| id | doaj-art-abc03e8d05624b548d7e72e4c141c548 |
| institution | DOAJ |
| issn | 2357-3716 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | Corporación Universitaria Republicana |
| record_format | Article |
| series | Revista Ingeniería, Matemáticas y Ciencias de la Información |
| spelling | doaj-art-abc03e8d05624b548d7e72e4c141c5482025-08-20T02:54:40ZengCorporación Universitaria RepublicanaRevista Ingeniería, Matemáticas y Ciencias de la Información2357-37162025-01-01122314715810.21017/rimci.1135Study of Statistical Convergence of Triple Sequences in a Topological Space Birojit Das0https://orcid.org/0000-0001-7614-1051Apurba Debnath1https://orcid.org/0000-0002-0541-8241Carlos Granados2https://orcid.org/0009-0007-1305-7822Abdullah Aydin3https://orcid.org/0000-0002-0769-5752National Institute of Technology Warangal National Institute of Technology Agartala Universidad Nacional Abierta y a Distancia Mus Alparslan University & Middle East Technical University In this paper, we introduce statistical convergence of triple sequences which are defined in a topological space. Various results on statistically convergent triple sequences are produced by using the notion of triple natural density operator. Moreover, we initiate the concept of -convergence of triple sequence and establish the interrelationship among -convergence and -converegnce. We see that the first one implies the second one but it’s not vice-versa. But if we restrict the triple sequences to hold the property of first countability, we verify that these notions becomes equivalent. Finally, we prove that the family of all statistically convergent triple sequences under some conditions generates a topological structure within the topological space where they have been defined.https://ojs.urepublicana.edu.co/index.php/ingenieria/article/view/1135statistical convergencetriple sequencetopological space |
| spellingShingle | Birojit Das Apurba Debnath Carlos Granados Abdullah Aydin Study of Statistical Convergence of Triple Sequences in a Topological Space Revista Ingeniería, Matemáticas y Ciencias de la Información statistical convergence triple sequence topological space |
| title | Study of Statistical Convergence of Triple Sequences in a Topological Space |
| title_full | Study of Statistical Convergence of Triple Sequences in a Topological Space |
| title_fullStr | Study of Statistical Convergence of Triple Sequences in a Topological Space |
| title_full_unstemmed | Study of Statistical Convergence of Triple Sequences in a Topological Space |
| title_short | Study of Statistical Convergence of Triple Sequences in a Topological Space |
| title_sort | study of statistical convergence of triple sequences in a topological space |
| topic | statistical convergence triple sequence topological space |
| url | https://ojs.urepublicana.edu.co/index.php/ingenieria/article/view/1135 |
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