Tauberian theorems for the statistical deferred Cesàro summability of sequences of fuzzy numbers
UDC 517.521 We introduce the concept of statistical deferred Cesàro summability for sequences of fuzzy numbers and examine its fundamental properties within the framework of fuzzy number spaces. It is shown that every bounded and statistically convergent sequence is statistically deferred Cesàro sum...
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| Datum: | 2026 |
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| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | Englisch |
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Institute of Mathematics, NAS of Ukraine
2026
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| Online Zugang: | https://umj.imath.kiev.ua/index.php/umj/article/view/9569 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1871646562489204736 |
|---|---|
| author | Yıldırım, Ebrar Çanak, İbrahim Yıldırım, Ebrar Çanak, İbrahim |
| author_facet | Yıldırım, Ebrar Çanak, İbrahim Yıldırım, Ebrar Çanak, İbrahim |
| author_institution_txt_mv | [
{
"author": "Ebrar Yıldırım",
"institution": "Graduate School of Natural and Applied Sciences, Ege University, İzmir, Turkey"
},
{
"author": "İbrahim Çanak",
"institution": "Department of Mathematics, Ege University, İzmir, Turkey"
}
] |
| author_sort | Yıldırım, Ebrar |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2026-07-24T15:24:12Z |
| description | UDC 517.521
We introduce the concept of statistical deferred Cesàro summability for sequences of fuzzy numbers and examine its fundamental properties within the framework of fuzzy number spaces. It is shown that every bounded and statistically convergent sequence is statistically deferred Cesàro summable to the same fuzzy number provided that the deferred Cesàro mean is properly deferred, thus showing that this summability method agrees with statistical convergence. However, the converse of this statement is, in general, not true. This means that additional conditions are required for the statistical convergence to follow from the statistical deferred Cesàro summability. Furthermore, we establish necessary and sufficient Tauberian conditions under which the statistical convergence of a certain subsequence of a sequence of fuzzy numbers follows from its statistical deferred Cesàro summability. Unlike the existing Tauberian results for the Cesàro summability of fuzzy numbers, the present work deals with the statistically deferred framework, which requires the use of essentially different techniques. |
| doi_str_mv | 10.3842/umzh.v78i7-8.9569 |
| first_indexed | 2026-07-25T01:00:56Z |
| format | Article |
| fulltext | |
| id | umjimathkievua-article-9569 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | English |
| last_indexed | 2026-07-25T01:00:56Z |
| publishDate | 2026 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | |
| spelling | umjimathkievua-article-95692026-07-24T15:24:12Z Tauberian theorems for the statistical deferred Cesàro summability of sequences of fuzzy numbers Tauberian theorems for the statistical deferred Cesàro summability of sequences of fuzzy numbers Yıldırım, Ebrar Çanak, İbrahim Yıldırım, Ebrar Çanak, İbrahim Deferred Ces\`{a}ro means Tauberian theorems and conditions statistical deferred slow oscillation sequences of fuzzy numbers Deferred Ces\`{a}ro means Tauberian theorems and conditions statistical deferred slow oscillation sequences of fuzzy numbers UDC 517.5 UDC 517.521 We introduce the concept of statistical deferred Cesàro summability for sequences of fuzzy numbers and examine its fundamental properties within the framework of fuzzy number spaces. It is shown that every bounded and statistically convergent sequence is statistically deferred Cesàro summable to the same fuzzy number provided that the deferred Cesàro mean is properly deferred, thus showing that this summability method agrees with statistical convergence. However, the converse of this statement is, in general, not true. This means that additional conditions are required for the statistical convergence to follow from the statistical deferred Cesàro summability. Furthermore, we establish necessary and sufficient Tauberian conditions under which the statistical convergence of a certain subsequence of a sequence of fuzzy numbers follows from its statistical deferred Cesàro summability. Unlike the existing Tauberian results for the Cesàro summability of fuzzy numbers, the present work deals with the statistically deferred framework, which requires the use of essentially different techniques. УДК 517.521 Тауберові теореми для статистичної відкладеної сумовності Чезаро послідовностей нечітких чисел Введено поняття статистичної відкладеної сумовності Чезаро для послідовностей нечітких чисел і досліджено його основні властивості в просторах нечітких чисел. Показано, що кожна обмежена статистично збіжна послідовність є статистично відкладено сумовною за Чезаро до того самого нечіткого числа за умови належної відкладеності середнього Чезаро, що встановлює узгодженість цього методу підсумовування зі статистичною збіжністю. Водночас обернене твердження загалом є невірним, що свідчить про необхідність додаткових умов для того, щоб статистична збіжність випливала зі статистичної відкладеної сумовності Чезаро. Крім того, отримано необхідні та достатні тауберові умови, за яких статистична збіжність певної підпослідовності послідовності нечітких чисел випливає з її статистичної відкладеної сумовності Чезаро. На відміну від наявних тауберових результатів для сумовності Чезаро нечітких чисел, ми розглядаємо статистично відкладену схему, що потребує істотно інших методів дослідження. Institute of Mathematics, NAS of Ukraine 2026-07-24 Article Article https://umj.imath.kiev.ua/index.php/umj/article/view/9569 10.3842/umzh.v78i7-8.9569 Ukrains’kyi Matematychnyi Zhurnal; Vol. 78 No. 7-8 (2026); 617–618 Український математичний журнал; Том 78 № 7-8 (2026); 617–618 1027-3190 en https://umj.imath.kiev.ua/index.php/umj/article/view/9569/10694 Copyright (c) 2026 Ebrar Yıldırım, İbrahim Çanak |
| spellingShingle | Yıldırım, Ebrar Çanak, İbrahim Yıldırım, Ebrar Çanak, İbrahim Tauberian theorems for the statistical deferred Cesàro summability of sequences of fuzzy numbers |
| title | Tauberian theorems for the statistical deferred Cesàro summability of sequences of fuzzy numbers |
| title_alt | Tauberian theorems for the statistical deferred Cesàro summability of sequences of fuzzy numbers |
| title_full | Tauberian theorems for the statistical deferred Cesàro summability of sequences of fuzzy numbers |
| title_fullStr | Tauberian theorems for the statistical deferred Cesàro summability of sequences of fuzzy numbers |
| title_full_unstemmed | Tauberian theorems for the statistical deferred Cesàro summability of sequences of fuzzy numbers |
| title_short | Tauberian theorems for the statistical deferred Cesàro summability of sequences of fuzzy numbers |
| title_sort | tauberian theorems for the statistical deferred cesàro summability of sequences of fuzzy numbers |
| topic_facet | Deferred Ces\`{a}ro means Tauberian theorems and conditions statistical deferred slow oscillation sequences of fuzzy numbers Deferred Ces\`{a}ro means Tauberian theorems and conditions statistical deferred slow oscillation sequences of fuzzy numbers UDC 517.5 |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/9569 |
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